oli29 wrote:

Hey Guys,

How come that I can not just add all single possibilities of how the committee is structured e.g. (All Females) + (3 Females 1 Male) + (2 Females 2 Males) + (1 Female 3 Males):

n= 6C4 + (6C3 *6C1) + (6C2 * 6C2) + (6C1 * 6C3) ?

Hi

oli29,

Your method is perfectly fine. The above expression would give you the same result, but as you notice that the calculation becomes tedious.

There is a small trick to solve such problems: Use

Complementary Method.

Total number of ways to choose four representative = (4 Females, 0 Males) + (3 Females, 1 Male) + (2 Females, 2 Males) + (1 Female, 3 Males) + (0 Females, 4 Males).

Please note that required event = Total - (0 Females, 4 Males).

Please refer the post by

TheOutlawTorn.

Hope this helps.