A committe of 7 members needs to be formed. The members are chosen randomly from 10 parents, 5 teenagers, and 4 adults without children. ---->What is the probability that the adults without...

A committe of 7 members needs to be formed. The members are chosen randomly from 10 parents, 5 teenagers, and 4 adults without children. ---->

What is the probability that the adults without children are chosen for the committee?

thilina-g | Certified Educator

There are 7 places in the committee. The number of adults without children is 4. The probability that all of them are chosen to the committee can be found as below.

There are 19 persons altogether.

The total number of ways that committee can be selected without restriction

=` ^19C_7`

`= 50388`

The number of ways that committee can be formed with all adults without children are,

`= ^4C_4 xx ^15C_3`

`= 1 xx 455`

`= 455`

Therefore, the probability that all of the adults without children  are chosen to the committee is,

` = 455/50388`

` = 0.0090299`

Therefore the answer is 0.90299 %.

mlehuzzah | Certified Educator

I'm guessing you mean that *all* of the adults without children are chosen for the committee:

The probability is the number of committees containing all 4 childless adults, divided by the number of possible committees.

The total number of possible committees is C(19,7)=50388

To count the number of committees containing all 4 childless adults, think of the 7 spots available.  4 of those spots are "reserved" for the childless adults.  That leaves 3 spots open on the committee, and 15 possible people to fill those spots.  So it's really like you are choosing a "sub committe" of 3 people from 15 people, and then adding to that the 4 childless adults.

So: the committees with all 4 childless adults is C(15,3) = 455

So the probability is 455/50388 = .009