SOLUTION: In how many ways can 2 men,4 women,3 boys and 3 girls be selected from 6 men, 8 women,4 boys and 5 girls if no restrictions are imposed

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Question 1058727: In how many ways can 2 men,4 women,3 boys and 3 girls be selected from 6 men, 8 women,4 boys and 5 girls if no restrictions are imposed
Answer by ikleyn(52786) About Me  (Show Source):
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In how many ways can 2 men, 4 women, 3 boys and 3 girls be selected from 6 men, 8 women, 4 boys and 5 girls if no restrictions are imposed
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C%5B6%5D%5E2 = %286%2A5%29%2F%281%2A2%29 = 3*5 = 15 ways for men.


C%5B8%5D%5E4 = %288%2A7%2A6%2A5%29%2F%281%2A2%2A3%2A4%29 = 7*2*5 = 70 ways for women.


C%5B4%5D%5E3 = 4 ways for boys.


C%5B5%5D%5E3 = %285%2A4%2A3%29%2F%281%2A2%2A3%29 = 5*2 = 10 ways for girls.


In total, 15*70*4*10 ways.

This problem is about combinations.

On combinations, see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".