Mixing
In how many ways you can pick 4 different items from 7 different items
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Basically, my task is to calculate how many undersets(⊆, dont know the english term)? have odd numbers in them from set={1,2,3,4,5,6,7}. For example {1}, {1,5,6}, {1,2,3,4,5,6,7} should be counted in.
I thought I can calculate how many containing odd number with 1 element, 2 elements so on. I calculated (A lower number 4 upper number 1)=4, so 4 with 1 element, then (A lower number 4 upper number 1)*6=24, so 24 with 2 elements, but I tried looking at all the cases and i got 18 (12 13 14 15 16 17)(32 34 35 36 37) (52 54 56 57) (72 74 76). What's wrong?
combinatorics
asked Jan 1 at 19:12
ImBeginningToFeelLikeAMathGodImBeginningToFeelLikeAMathGod
31
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add a comment |
$begingroup$
Basically, my task is to calculate how many undersets(⊆, dont know the english term)? have odd numbers in them from set={1,2,3,4,5,6,7}. For example {1}, {1,5,6}, {1,2,3,4,5,6,7} should be counted in.
I thought I can calculate how many containing odd number with 1 element, 2 elements so on. I calculated (A lower number 4 upper number 1)=4, so 4 with 1 element, then (A lower number 4 upper number 1)*6=24, so 24 with 2 elements, but I tried looking at all the cases and i got 18 (12 13 14 15 16 17)(32 34 35 36 37) (52 54 56 57) (72 74 76). What's wrong?
combinatorics
asked Jan 1 at 19:12
ImBeginningToFeelLikeAMathGodImBeginningToFeelLikeAMathGod
31
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1
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Try subtracting all the subsets with only even elements from the total number of subsets. This might be easier. The total number of subsets of a list ${x_1,x_2,x_3,...,x_n}$ is $2^n-1$ if we don't count the empty set.
$endgroup$
– D.B.
Jan 1 at 19:17
add a comment |
$begingroup$
Basically, my task is to calculate how many undersets(⊆, dont know the english term)? have odd numbers in them from set={1,2,3,4,5,6,7}. For example {1}, {1,5,6}, {1,2,3,4,5,6,7} should be counted in.
I thought I can calculate how many containing odd number with 1 element, 2 elements so on. I calculated (A lower number 4 upper number 1)=4, so 4 with 1 element, then (A lower number 4 upper number 1)*6=24, so 24 with 2 elements, but I tried looking at all the cases and i got 18 (12 13 14 15 16 17)(32 34 35 36 37) (52 54 56 57) (72 74 76). What's wrong?
combinatorics
asked Jan 1 at 19:12
ImBeginningToFeelLikeAMathGodImBeginningToFeelLikeAMathGod
31
$endgroup$
Basically, my task is to calculate how many undersets(⊆, dont know the english term)? have odd numbers in them from set={1,2,3,4,5,6,7}. For example {1}, {1,5,6}, {1,2,3,4,5,6,7} should be counted in.
I thought I can calculate how many containing odd number with 1 element, 2 elements so on. I calculated (A lower number 4 upper number 1)=4, so 4 with 1 element, then (A lower number 4 upper number 1)*6=24, so 24 with 2 elements, but I tried looking at all the cases and i got 18 (12 13 14 15 16 17)(32 34 35 36 37) (52 54 56 57) (72 74 76). What's wrong?
combinatorics
combinatorics
asked Jan 1 at 19:12
ImBeginningToFeelLikeAMathGodImBeginningToFeelLikeAMathGod
31
asked Jan 1 at 19:12
ImBeginningToFeelLikeAMathGodImBeginningToFeelLikeAMathGod
31
asked Jan 1 at 19:12
ImBeginningToFeelLikeAMathGodImBeginningToFeelLikeAMathGod
31
asked Jan 1 at 19:12
ImBeginningToFeelLikeAMathGodImBeginningToFeelLikeAMathGod
31
asked Jan 1 at 19:12
ImBeginningToFeelLikeAMathGodImBeginningToFeelLikeAMathGod
31
31
1
$begingroup$
Try subtracting all the subsets with only even elements from the total number of subsets. This might be easier. The total number of subsets of a list ${x_1,x_2,x_3,...,x_n}$ is $2^n-1$ if we don't count the empty set.
$endgroup$
– D.B.
Jan 1 at 19:17
add a comment |
1
$begingroup$
Try subtracting all the subsets with only even elements from the total number of subsets. This might be easier. The total number of subsets of a list ${x_1,x_2,x_3,...,x_n}$ is $2^n-1$ if we don't count the empty set.
$endgroup$
– D.B.
Jan 1 at 19:17
1
1
$begingroup$
Try subtracting all the subsets with only even elements from the total number of subsets. This might be easier. The total number of subsets of a list ${x_1,x_2,x_3,...,x_n}$ is $2^n-1$ if we don't count the empty set.
$endgroup$
– D.B.
Jan 1 at 19:17
$begingroup$
Try subtracting all the subsets with only even elements from the total number of subsets. This might be easier. The total number of subsets of a list ${x_1,x_2,x_3,...,x_n}$ is $2^n-1$ if we don't count the empty set.
$endgroup$
– D.B.
Jan 1 at 19:17
add a comment |
1 Answer
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The total number of subsets are $2^7$
The number of subsets made totally out of even integers are $2^3$ therefore the number of subsets with some odd integers is $2^7-2^3=120$
answered Jan 1 at 19:20
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
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$begingroup$
The total number of subsets are $2^7$
The number of subsets made totally out of even integers are $2^3$ therefore the number of subsets with some odd integers is $2^7-2^3=120$
answered Jan 1 at 19:20
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
$endgroup$
add a comment |
$begingroup$
The total number of subsets are $2^7$
The number of subsets made totally out of even integers are $2^3$ therefore the number of subsets with some odd integers is $2^7-2^3=120$
answered Jan 1 at 19:20
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
$endgroup$
add a comment |
$begingroup$
The total number of subsets are $2^7$
The number of subsets made totally out of even integers are $2^3$ therefore the number of subsets with some odd integers is $2^7-2^3=120$
answered Jan 1 at 19:20
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
$endgroup$
The total number of subsets are $2^7$
The number of subsets made totally out of even integers are $2^3$ therefore the number of subsets with some odd integers is $2^7-2^3=120$
answered Jan 1 at 19:20
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
answered Jan 1 at 19:20
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
answered Jan 1 at 19:20
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
answered Jan 1 at 19:20
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.5k42061
41.5k42061
add a comment |
add a comment |
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1
$begingroup$
Try subtracting all the subsets with only even elements from the total number of subsets. This might be easier. The total number of subsets of a list ${x_1,x_2,x_3,...,x_n}$ is $2^n-1$ if we don't count the empty set.
$endgroup$
– D.B.
Jan 1 at 19:17