Committee members

Probability Level pending

A committee of 4 is to be chosen from a number of people, two of whom are women. If the probability of both women being on the committee is twice that of no women being on the committee, how many people are available to be chosen from?


The answer is 7.

K P by k p , 43, United Kingdom

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

K P
Apr 18, 2016

total ways = nC4,

women = (n-2)C2 we only need to chose a pair,

No women = (n-2)C4,

so 2[(n-2)C4 =(n-2)C2,

thus 2( ( n − 2 ) ! ( n − 6 ) ! 4 ! \frac{(n-2)!}{(n-6)!4!} = ( n − 2 ) ! ( n − 4 ) ! 2 ! \frac{(n-2)!}{(n-4)!2!}

2.2 ! 4 ! \frac{2.2!}{4!} = ( n − 6 ) ! ( n − 4 ) ! \frac{(n-6)!}{(n-4)!}

1 6 \frac{1}{6} = 1 ( n − 4 ) ( n − 5 ) \frac{1}{(n-4)(n-5)}

6=(n-4)(n-5)

0=(n-7)(n-2)

Hence n=7

n=2 is an insufficent answer since we need a committee of 4

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...