A club consists of 16 men and 19 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people? (Round the answer to five decimal places.)

Question

The Answer is blank x 10 to the 11th power ways

Answer 1

I guess that the number of men and women doesn't matter so they're just 35 all.
My answer is 35P4 + 31C6.
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I used permutations for the pres~sec b'cse they have diff roles, not like the advisory committee.
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Email me at ust008332@gmail if you found a better answer.

Answer 2

The number of men and women is irrelevant (unless they've got any rules that restrict the gender of any of those posts), so all that matters is that there are (16+19)=35 people from which to choose. The instruction to round the answer to five decimal places is a red herring, as the answer must be an integer - even if you do have to express it in scientific notation because it's so large. Assuming that nobody can occupy more than one position on the committee, the number of permutations should be 35 x 34 x 33 x 32 x Choose(6 from 31), which is 35 x 34 x 33 x 32 x (31! / (6! x 25!)), which I reckon is 2.31310 x (10^13).

Answer 3

Oops - I can't do permutations properly: it's 25 times too big. That last calculation should have been 9.25240 x (10^11). Sorry!

Answer 4

Thank you all Very Much!