Mixing
How many ways to achieve a multiple of $5$ numbers between $1$ and $8$ which are not unique?
$begingroup$
This question comes from the Faridpur Olympiad $2017$.
Text:
$9)$ The numbers $1$ to $8$ are written on seven balls. Miyad took five balls from there such that if he multiplies the numbers of the balls and then say it to Mursalin, then Mursalin can't say the number of the balls surely. How many ways can Miyad do this?
My attempt:
I noticed that it was only possible if Mursalin is confused between:
$1) (a,b,c, 1, 8)$ and $(a,b,c, 2, 4)$
$2) (a,b,c, 2, 3)$ and $(a,b,c, 1, 6)$
$3) (a,b,c, 4, 3)$ and $(a,b,c, 2, 6)$
$4) (a,b,c, 8, 3)$ and $(a,b,c, 4, 6)$
Is there any other case? How can I calculate the number of possible combinations? Also, the part about "(t)he numbers $1$ to $8$ are written on seven balls" confuses me. Is it supposed to be eight balls?
combinatorics
asked Jan 31 at 17:04
Mohammad Zuhair KhanMohammad Zuhair Khan
1,6912625
$endgroup$
add a comment |
$begingroup$
This question comes from the Faridpur Olympiad $2017$.
Text:
$9)$ The numbers $1$ to $8$ are written on seven balls. Miyad took five balls from there such that if he multiplies the numbers of the balls and then say it to Mursalin, then Mursalin can't say the number of the balls surely. How many ways can Miyad do this?
My attempt:
I noticed that it was only possible if Mursalin is confused between:
$1) (a,b,c, 1, 8)$ and $(a,b,c, 2, 4)$
$2) (a,b,c, 2, 3)$ and $(a,b,c, 1, 6)$
$3) (a,b,c, 4, 3)$ and $(a,b,c, 2, 6)$
$4) (a,b,c, 8, 3)$ and $(a,b,c, 4, 6)$
Is there any other case? How can I calculate the number of possible combinations? Also, the part about "(t)he numbers $1$ to $8$ are written on seven balls" confuses me. Is it supposed to be eight balls?
combinatorics
asked Jan 31 at 17:04
Mohammad Zuhair KhanMohammad Zuhair Khan
1,6912625
$endgroup$
$begingroup$
The statement, "The numbers $1$ to $8$ are written on seven balls," seems ambiguous to me. Does it mean that one of the numbers is missing? Does is mean that each number is written on seven different balls? Is it supposed to say eight balls? I don't see how to tell.
$endgroup$
– saulspatz
Jan 31 at 17:27
$begingroup$
Nor do I which is why I included the image. The bengali suggests that one number is skipped at random. However, I don't see how choosing 5 out of 7 is different from choosing 5 out of 8.
$endgroup$
– Mohammad Zuhair Khan
Jan 31 at 17:29
add a comment |
$begingroup$
This question comes from the Faridpur Olympiad $2017$.
Text:
$9)$ The numbers $1$ to $8$ are written on seven balls. Miyad took five balls from there such that if he multiplies the numbers of the balls and then say it to Mursalin, then Mursalin can't say the number of the balls surely. How many ways can Miyad do this?
My attempt:
I noticed that it was only possible if Mursalin is confused between:
$1) (a,b,c, 1, 8)$ and $(a,b,c, 2, 4)$
$2) (a,b,c, 2, 3)$ and $(a,b,c, 1, 6)$
$3) (a,b,c, 4, 3)$ and $(a,b,c, 2, 6)$
$4) (a,b,c, 8, 3)$ and $(a,b,c, 4, 6)$
Is there any other case? How can I calculate the number of possible combinations? Also, the part about "(t)he numbers $1$ to $8$ are written on seven balls" confuses me. Is it supposed to be eight balls?
combinatorics
asked Jan 31 at 17:04
Mohammad Zuhair KhanMohammad Zuhair Khan
1,6912625
$endgroup$
This question comes from the Faridpur Olympiad $2017$.
Text:
$9)$ The numbers $1$ to $8$ are written on seven balls. Miyad took five balls from there such that if he multiplies the numbers of the balls and then say it to Mursalin, then Mursalin can't say the number of the balls surely. How many ways can Miyad do this?
My attempt:
I noticed that it was only possible if Mursalin is confused between:
$1) (a,b,c, 1, 8)$ and $(a,b,c, 2, 4)$
$2) (a,b,c, 2, 3)$ and $(a,b,c, 1, 6)$
$3) (a,b,c, 4, 3)$ and $(a,b,c, 2, 6)$
$4) (a,b,c, 8, 3)$ and $(a,b,c, 4, 6)$
Is there any other case? How can I calculate the number of possible combinations? Also, the part about "(t)he numbers $1$ to $8$ are written on seven balls" confuses me. Is it supposed to be eight balls?
combinatorics
combinatorics
asked Jan 31 at 17:04
Mohammad Zuhair KhanMohammad Zuhair Khan
1,6912625
asked Jan 31 at 17:04
Mohammad Zuhair KhanMohammad Zuhair Khan
1,6912625
asked Jan 31 at 17:04
Mohammad Zuhair KhanMohammad Zuhair Khan
1,6912625
asked Jan 31 at 17:04
Mohammad Zuhair KhanMohammad Zuhair Khan
1,6912625
asked Jan 31 at 17:04
Mohammad Zuhair KhanMohammad Zuhair Khan
1,6912625
1,6912625
$begingroup$
The statement, "The numbers $1$ to $8$ are written on seven balls," seems ambiguous to me. Does it mean that one of the numbers is missing? Does is mean that each number is written on seven different balls? Is it supposed to say eight balls? I don't see how to tell.
$endgroup$
– saulspatz
Jan 31 at 17:27
$begingroup$
Nor do I which is why I included the image. The bengali suggests that one number is skipped at random. However, I don't see how choosing 5 out of 7 is different from choosing 5 out of 8.
$endgroup$
– Mohammad Zuhair Khan
Jan 31 at 17:29
add a comment |
$begingroup$
The statement, "The numbers $1$ to $8$ are written on seven balls," seems ambiguous to me. Does it mean that one of the numbers is missing? Does is mean that each number is written on seven different balls? Is it supposed to say eight balls? I don't see how to tell.
$endgroup$
– saulspatz
Jan 31 at 17:27
$begingroup$
Nor do I which is why I included the image. The bengali suggests that one number is skipped at random. However, I don't see how choosing 5 out of 7 is different from choosing 5 out of 8.
$endgroup$
– Mohammad Zuhair Khan
Jan 31 at 17:29
$begingroup$
The statement, "The numbers $1$ to $8$ are written on seven balls," seems ambiguous to me. Does it mean that one of the numbers is missing? Does is mean that each number is written on seven different balls? Is it supposed to say eight balls? I don't see how to tell.
$endgroup$
– saulspatz
Jan 31 at 17:27
$begingroup$
The statement, "The numbers $1$ to $8$ are written on seven balls," seems ambiguous to me. Does it mean that one of the numbers is missing? Does is mean that each number is written on seven different balls? Is it supposed to say eight balls? I don't see how to tell.
$endgroup$
– saulspatz
Jan 31 at 17:27
$begingroup$
Nor do I which is why I included the image. The bengali suggests that one number is skipped at random. However, I don't see how choosing 5 out of 7 is different from choosing 5 out of 8.
$endgroup$
– Mohammad Zuhair Khan
Jan 31 at 17:29
$begingroup$
Nor do I which is why I included the image. The bengali suggests that one number is skipped at random. However, I don't see how choosing 5 out of 7 is different from choosing 5 out of 8.
$endgroup$
– Mohammad Zuhair Khan
Jan 31 at 17:29
add a comment |
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$begingroup$
The statement, "The numbers $1$ to $8$ are written on seven balls," seems ambiguous to me. Does it mean that one of the numbers is missing? Does is mean that each number is written on seven different balls? Is it supposed to say eight balls? I don't see how to tell.
$endgroup$
– saulspatz
Jan 31 at 17:27
$begingroup$
Nor do I which is why I included the image. The bengali suggests that one number is skipped at random. However, I don't see how choosing 5 out of 7 is different from choosing 5 out of 8.
$endgroup$
– Mohammad Zuhair Khan
Jan 31 at 17:29