probability

Question

We want to select a committee of five members from a group of seven women and six men. The order of selection is irrelevant.

How many committees can we make with fewer men than women? Suggestion: There could be three women and two men, four women and one man, or five women.

 

please show me how to get answer and give answer, I am a non trad student trying to learn all this new stuff...need to see how answer is attained.

Answer 1

Possisble committee compositions (presented in (M,W) order:

(0,5)

(1,4)

(2,3)

Each of the above has # Men < # Women, and there are no other possibilities.

 

The number of ways that these may be chosen are, respectively:

6C0 times 7C5,

6C1 times 7C4,

and 6C2 tiumes 7C3.

 

Compute the three above values, and total them to get the answer.