Question

A city council consists of seven Democratsand eight Republicans. If a committee ofseven people is selected, find the probabilityof selecting three Democrats and fourRepublicans.(Type a fraction. Simplify your answer.)

Answer 1

A city council consists of seven Democrats

and eight Republicans. If a committee of

seven people is selected, find the probability

of selecting three Democrats and four

Republicans.

step 1

we have seven Democrats------> select three Democrats

Find out 3C7

`3C7=(7!)/(3!(7-3)!)=35`

step 2

eight Republicans ------> select four Republicans

Find out 4C8

`4C8=(8!)/(4!(8-4)!)=70`

step 3

Total possible favorable outcomes

35*70=2,450

total possible outcomes

Find out 7C15

`7C15=(15!)/(7!(15-7)!)=6,435`

therefore

the probability is

P=2,450/6,435

simplify

P=490/1,287