Question

A total of 1010 students are entered in a drawing to win 33 identical prizes. The group of students is composed of 66 boys and 44 girls. What is the probability that 22 boys and 11 girl win prizes?

Answer 1

Answer: 0.75

Explanation:

Given : A total of 10 students are entered in a drawing to win 3 identical prizes.

The group of students is composed of 6 boys and 4 girls.

We know that the number of combinations of n things taking r at a time is given by :-

`^nC_r=(n!)/((n-r)!r!)`

The number of ways to choose any 3 out of 10 to win prizes will be :-

`^(10)C_r=(10!)/((10-3)!3!)=(10*9*8*7!)/(7!*6)=120` (1)

The number of ways to choose 2 boys and 1 girl to win prizes will be :-

`^6C_2*^4C_2=(6!)/(2!4!)*(4!)/(2!2!)\\\\=15*6=90` (2)

Now, the probability that 2 boys and 1 girl win prizes will be :-

`(90)/(120)=0.75` [ Divide (2) by (1) ]

Hence, the required probability = 0.75