# pleas help. probability.

• Jan 25th 2009, 10:03 PM
Big-K
pleas help. probability.
How many diff. 3-member comittees can be chosen if the committee cannot have all females or all males?

35 members (15 females & 20 males)
3 member committee: President, VP, Treasurer

back of the book says 29,700.
but i keep getting different answers.

• Jan 25th 2009, 10:20 PM
mr fantastic
Quote:

Originally Posted by Big-K
How many diff. 3-member comittees can be chosen if the committee cannot have all females or all males?

35 members (15 females & 20 males)
3 member committee: President, VP, Treasurer

back of the book says 29,700.
but i keep getting different answers.

In the committe you can have either 1 female and 2 males or 2 females and 1 male:

${15 \choose 1} \cdot {20 \choose 2} + {15 \choose 2} \cdot {20 \choose 1} = \, ....$

Then you have to multiply by 3! = 6 (why?)