Question

Two companies have sent representatives to an industry conference. The first company sent 12 representatives and the second company sent 20 representatives. Only 22 will be given the chance to make presentations. What is the probability that exactly 10 representatives from the first company and 12 representatives from the second company will be chosen?

Answer 1

0.1289

Explanation:

Given that two companies have sent representatives to an industry conference.

The first company sent 12 representatives and the second company sent 20 representatives

Selecting any 22 out of these 32 can be done in
`32C22 ==(32!)/((22!(32−22)!)) \\= 64512240`

Favourable outcomes = No of ways of selecting 10 from I and 12 from II

=
`12C10(20C12) =66(125970) \\=8314020`

Probability required =
`(8314020)/(64512240) \\=0.1289`