Question

A man has 5 female and 7 male friends and his wife has 7 female and...

A man has 5 female and 7 male friends and his wife has 7 female and 5 male friends. In how many ways can they invite 6 males and 6 females if husband and wife are to invite 6 friends each?

this is final Answer. 267,148.but i need method

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Man has 7 Male and 5 Female Friends

Wife has 5 Male and 7 Female Friends

Total 6 Male and 6 Females are to be invited with both Man and Wife Inviting 6 Friends each.

Below are all the possible combinations (scenarios)

Scenario 7 is not possible as Man as max 5 Female Friends and Wife has maximum 5 Male Friends

Total Combinations are calculated as ∑ (product of Man Combination * Wife Combination)

Example:

Scenario 1:

Man = 7C6*5C0 = 7*1 = 7

Wife = 5C0*7C6 = 1*7 = 7

Total = Man * Wife = 7*7

Hence,

All possible combinations = 267148

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