Question

There are names for 30 people in a hat, 10 are students, 3 administrators and the rest are teachers. If you select 4 names at random without replacement, what is the probability that you get two students and two teachers?

Answer 1

There are 30 people. So N=30

There are 10 students , 3 administrators , and [ 30 - ( 10+3)] = 17 teacher

We select 4 names without replacement

We can get 2 students in 10C2 ways.

We can get 2 teachers in 17C2 ways

We can select any 4 people from those all 30 people, in 30C4 ways.

[ here C stands for Combination]

So required probability of

P[ selecting 4 people and getting 2 student and 2 teacher]

= [ 10C2 ×17C2]÷ 30C4

={45×136}÷27405

= 0.2233. [ approximately]