Mixing
Combination of 3 coin flips
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Friends, for 3 coin flips, the total possible outcomes are 8, given by 2x2x2. But if the order does not matter for me, i should find the combination, which is 4 (TTT, HHH, HHT, HTT).
For 3 coin flips, i can list out the 8 possible outcomes and cross out the repeats to find the number of combination. What if i am to do 10 coin flips? How can i find the number of combination w/o listing all possible outcomes and then crossing out the repeats?
Appreciate your help.
permutations combinations
asked Apr 12 '18 at 4:18
Jorge MercentJorge Mercent
114
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add a comment |
$begingroup$
Friends, for 3 coin flips, the total possible outcomes are 8, given by 2x2x2. But if the order does not matter for me, i should find the combination, which is 4 (TTT, HHH, HHT, HTT).
For 3 coin flips, i can list out the 8 possible outcomes and cross out the repeats to find the number of combination. What if i am to do 10 coin flips? How can i find the number of combination w/o listing all possible outcomes and then crossing out the repeats?
Appreciate your help.
permutations combinations
asked Apr 12 '18 at 4:18
Jorge MercentJorge Mercent
114
$endgroup$
add a comment |
$begingroup$
Friends, for 3 coin flips, the total possible outcomes are 8, given by 2x2x2. But if the order does not matter for me, i should find the combination, which is 4 (TTT, HHH, HHT, HTT).
For 3 coin flips, i can list out the 8 possible outcomes and cross out the repeats to find the number of combination. What if i am to do 10 coin flips? How can i find the number of combination w/o listing all possible outcomes and then crossing out the repeats?
Appreciate your help.
permutations combinations
asked Apr 12 '18 at 4:18
Jorge MercentJorge Mercent
114
$endgroup$
Friends, for 3 coin flips, the total possible outcomes are 8, given by 2x2x2. But if the order does not matter for me, i should find the combination, which is 4 (TTT, HHH, HHT, HTT).
For 3 coin flips, i can list out the 8 possible outcomes and cross out the repeats to find the number of combination. What if i am to do 10 coin flips? How can i find the number of combination w/o listing all possible outcomes and then crossing out the repeats?
Appreciate your help.
permutations combinations
permutations combinations
asked Apr 12 '18 at 4:18
Jorge MercentJorge Mercent
114
asked Apr 12 '18 at 4:18
Jorge MercentJorge Mercent
114
asked Apr 12 '18 at 4:18
Jorge MercentJorge Mercent
114
asked Apr 12 '18 at 4:18
Jorge MercentJorge Mercent
114
asked Apr 12 '18 at 4:18
Jorge MercentJorge Mercent
114
114
add a comment |
add a comment |
1 Answer
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$begingroup$
For $10$ coins, there is one configuration with $0$ head, there is one configuration with $1$ head, one configuration with $2$ heads, one configuration with $3$ heads and so on. $ldots$, one configuration with $10$ heads.
In general, if you have $n$ coins, you have $n+1$ combinations.
answered Apr 12 '18 at 4:20
Siong Thye GohSiong Thye Goh
103k1468120
$endgroup$
$begingroup$
Thank you! An additional quick question: the 8 outcomes in 3 coinflips, do we call them permutations or combinations?
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:33
$begingroup$
hmm... $THH$ and $HTT$ are different, so they can't be combinations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:34
$begingroup$
Ya...so i guess if i call them combinations, people wouldn't get angry..i suppose
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:38
$begingroup$
permutations cares about ordering, combinations doesn't. it should be permutations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:39
$begingroup$
Got it! The 4 (TTT, HHH, HHT, HTT) can be called combination, but the 8 should be called permutations, since outcomes of same result but different different order (exp. THH, HHT) are counted in the 8.
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:45
|
show 3 more comments
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
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active
oldest
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active
oldest
votes
$begingroup$
For $10$ coins, there is one configuration with $0$ head, there is one configuration with $1$ head, one configuration with $2$ heads, one configuration with $3$ heads and so on. $ldots$, one configuration with $10$ heads.
In general, if you have $n$ coins, you have $n+1$ combinations.
answered Apr 12 '18 at 4:20
Siong Thye GohSiong Thye Goh
103k1468120
$endgroup$
$begingroup$
Thank you! An additional quick question: the 8 outcomes in 3 coinflips, do we call them permutations or combinations?
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:33
$begingroup$
hmm... $THH$ and $HTT$ are different, so they can't be combinations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:34
$begingroup$
Ya...so i guess if i call them combinations, people wouldn't get angry..i suppose
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:38
$begingroup$
permutations cares about ordering, combinations doesn't. it should be permutations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:39
$begingroup$
Got it! The 4 (TTT, HHH, HHT, HTT) can be called combination, but the 8 should be called permutations, since outcomes of same result but different different order (exp. THH, HHT) are counted in the 8.
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:45
|
show 3 more comments
$begingroup$
For $10$ coins, there is one configuration with $0$ head, there is one configuration with $1$ head, one configuration with $2$ heads, one configuration with $3$ heads and so on. $ldots$, one configuration with $10$ heads.
In general, if you have $n$ coins, you have $n+1$ combinations.
answered Apr 12 '18 at 4:20
Siong Thye GohSiong Thye Goh
103k1468120
$endgroup$
$begingroup$
Thank you! An additional quick question: the 8 outcomes in 3 coinflips, do we call them permutations or combinations?
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:33
$begingroup$
hmm... $THH$ and $HTT$ are different, so they can't be combinations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:34
$begingroup$
Ya...so i guess if i call them combinations, people wouldn't get angry..i suppose
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:38
$begingroup$
permutations cares about ordering, combinations doesn't. it should be permutations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:39
$begingroup$
Got it! The 4 (TTT, HHH, HHT, HTT) can be called combination, but the 8 should be called permutations, since outcomes of same result but different different order (exp. THH, HHT) are counted in the 8.
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:45
|
show 3 more comments
$begingroup$
For $10$ coins, there is one configuration with $0$ head, there is one configuration with $1$ head, one configuration with $2$ heads, one configuration with $3$ heads and so on. $ldots$, one configuration with $10$ heads.
In general, if you have $n$ coins, you have $n+1$ combinations.
answered Apr 12 '18 at 4:20
Siong Thye GohSiong Thye Goh
103k1468120
$endgroup$
For $10$ coins, there is one configuration with $0$ head, there is one configuration with $1$ head, one configuration with $2$ heads, one configuration with $3$ heads and so on. $ldots$, one configuration with $10$ heads.
In general, if you have $n$ coins, you have $n+1$ combinations.
answered Apr 12 '18 at 4:20
Siong Thye GohSiong Thye Goh
103k1468120
answered Apr 12 '18 at 4:20
Siong Thye GohSiong Thye Goh
103k1468120
answered Apr 12 '18 at 4:20
Siong Thye GohSiong Thye Goh
103k1468120
answered Apr 12 '18 at 4:20
Siong Thye GohSiong Thye Goh
103k1468120
103k1468120
$begingroup$
Thank you! An additional quick question: the 8 outcomes in 3 coinflips, do we call them permutations or combinations?
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:33
$begingroup$
hmm... $THH$ and $HTT$ are different, so they can't be combinations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:34
$begingroup$
Ya...so i guess if i call them combinations, people wouldn't get angry..i suppose
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:38
$begingroup$
permutations cares about ordering, combinations doesn't. it should be permutations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:39
$begingroup$
Got it! The 4 (TTT, HHH, HHT, HTT) can be called combination, but the 8 should be called permutations, since outcomes of same result but different different order (exp. THH, HHT) are counted in the 8.
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:45
|
show 3 more comments
$begingroup$
Thank you! An additional quick question: the 8 outcomes in 3 coinflips, do we call them permutations or combinations?
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:33
$begingroup$
hmm... $THH$ and $HTT$ are different, so they can't be combinations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:34
$begingroup$
Ya...so i guess if i call them combinations, people wouldn't get angry..i suppose
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:38
$begingroup$
permutations cares about ordering, combinations doesn't. it should be permutations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:39
$begingroup$
Got it! The 4 (TTT, HHH, HHT, HTT) can be called combination, but the 8 should be called permutations, since outcomes of same result but different different order (exp. THH, HHT) are counted in the 8.
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:45
$begingroup$
Thank you! An additional quick question: the 8 outcomes in 3 coinflips, do we call them permutations or combinations?
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:33
$begingroup$
Thank you! An additional quick question: the 8 outcomes in 3 coinflips, do we call them permutations or combinations?
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:33
$begingroup$
hmm... $THH$ and $HTT$ are different, so they can't be combinations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:34
$begingroup$
hmm... $THH$ and $HTT$ are different, so they can't be combinations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:34
$begingroup$
Ya...so i guess if i call them combinations, people wouldn't get angry..i suppose
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:38
$begingroup$
Ya...so i guess if i call them combinations, people wouldn't get angry..i suppose
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:38
$begingroup$
permutations cares about ordering, combinations doesn't. it should be permutations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:39
$begingroup$
permutations cares about ordering, combinations doesn't. it should be permutations.
$endgroup$
– Siong Thye Goh
Apr 12 '18 at 4:39
$begingroup$
Got it! The 4 (TTT, HHH, HHT, HTT) can be called combination, but the 8 should be called permutations, since outcomes of same result but different different order (exp. THH, HHT) are counted in the 8.
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:45
$begingroup$
Got it! The 4 (TTT, HHH, HHT, HTT) can be called combination, but the 8 should be called permutations, since outcomes of same result but different different order (exp. THH, HHT) are counted in the 8.
$endgroup$
– Jorge Mercent
Apr 12 '18 at 4:45
|
show 3 more comments
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