Question

there are 20 boys and 10 girls in a class.if a committee of 6 is to be chosen at random having at least 2 boys and 2 girls then find the probability that there are 4 boys in the committee​

Answer 1

Answer:

In a class of 10 boys and 5 girls, a committee of 4 students has to be selected. We want to determine the probability that the committee contains at least 3 girls.

If the committee contains 3 girls, we have to choose 3 girls out of 5 and 1 boy out of 10. The number of ways in which this can be done is C(5,3)⋅C(10,1)

=5!3!2!⋅10!1!9!=10×10=100.

If the committee contains 4 girls, we have to choose 4 girls out of 5 and 0 boy out of 10. The number of ways in which this can be done is C(5,4)⋅C(10,0)

=5!4!1!⋅10!0!10!=5×1=5.

⇒ The number of ways in which the committee can contain at least 3 girls is 100+5=105.

The number of ways in which the committee of 4 can be formed from 15 students is C(15,4)=15!4!11!=1365.

⇒ The probability that the committee contains at least 3 girls is 1051365=113.