Question 21

# Ashish is studying late into the night and is hungry. He opens his mother’s snack cupboard without switching on the lights, knowing that his mother has kept 10 packets of chips and biscuits in the cupboard. He pulls out 3 packets from the cupboard, and all of them turn out to be chips. What is the probability that the snack cupboard contains 1 packet of biscuits and 9 packets of chips?

Solution

We are given that C+B = 10
Thus, the cases are C=3 and B = 7
C = 4 and B = 6
C = 5 and B = 5
C = 6 and B = 4
C = 7 and B = 3
C = 8 and B = 2
C = 9 and B = 1
C = 10 and B = 0
Our required case = C = 9 and B = 1
Thus, the required probability = $$\dfrac{^9C_3}{^{10}C_{3}+^9C_3+^8C_3+^7C_3+^6C_3+^5C_3+^4C_3+^3C_3}$$
= $$\dfrac{14}{55}$$
Hence, option C is the correct answer.