0
$\begingroup$

An 8-persons committee is to be formed out of a group of 15 women and 12 men. In how many ways can the committee be chosen if there must be at least two men?

Please check my answer

I started the problem by finding all possible committees without gender concern that is

$$\binom{27}{8}$$

and I am not sure how to find answer directly. I choose to find from the case that violates the condition that is

$$\binom{12}{3}\binom{15}{5}$$

the answer is

$$\binom{27}{8}-\binom{12}{3}\binom{15}{5}$$

$\endgroup$
  • $\begingroup$ I have tried to improve your text. In particular a title should be synthetic, not contain the detailed statement of the problem. $\endgroup$ – Jean Marie Oct 8 '17 at 7:07
  • $\begingroup$ Why edit my question ? $\endgroup$ – Lingnoi401 Oct 8 '17 at 7:07
  • $\begingroup$ Um,I have gotten down vote by after someone edit my question without remove full text of my question with and make question is not clear like this Please re-edit my question $\endgroup$ – Lingnoi401 Oct 8 '17 at 7:11
  • 1
    $\begingroup$ The downvote (not mine) has nothing to do with the editing of your question. I am sorry to say that I am pretty certain that the level of english is quite better now than it was at first... I think that the downvote (that I do not approve) is because your solution is far from being exact. (Ctd...) $\endgroup$ – Jean Marie Oct 8 '17 at 7:12
  • $\begingroup$ I mean I had had downvote in a long time ago because it make question was not clear similiar like this question sorry for my bad english skill $\endgroup$ – Lingnoi401 Oct 8 '17 at 7:16
4
$\begingroup$
  • $\;\binom{12}{0}\binom{15}{8}$ committees with $0$ men.
  • $\;\binom{12}{1}\binom{15}{7}$ committees with $1$ man.

Hence the number of committees with at least $2$ men is $$ {\small{\binom{27}{8}}}-\left( {\small{\binom{12}{0}}}{\small{\binom{15}{8}}} + {\small{\binom{12}{1}}}{\small{\binom{15}{7}}} \right) $$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.