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?
Explanation:
There are at least three packets of chips in the cupboard. There are 10 packets in all.
∴ (Number of packets of chips, Number of packets of biscuits) ≡ (3, 7) or (4, 6) or (5, 5) or (6, 4) or (7, 3) or (8, 2) or (9, 1) or (10, 0)
The number of ways in which three packets of chips can be drawn 3C3 + 4C3 + 5C3 + 6C3 + 7C3 + 8C3 + 9C3 + 10C3 = 330
The number of ways in which three packets of chips can be drawn when there are 9 packets of chips = 9C3 = 84
∴ Required probability = 84330 = 1455
Hence, option (c).
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