Single answer type questions
An elevator starts with 7 persons and stops at 9 floors. Then the probability that exactly two persons
alight in one floor and the rest in different floors is
21x8 C
160 x 72
a)
b)
d)
97
97
95
21x8 Pg
320 x 72
95
c)
Answers
Given : An elevator starts with 7 persons and stops at 9 floors.
To Find : the probability that exactly two persons
alight in one floor and the rest in different floors is
Solution:
An elevator starts with 7 persons and stops at 9 floors.
Each person can choose any of 9 floors
Hence 9⁷ ways
exactly two persons alight in one floor and rest in different floors
2 persons can be selected in ⁷C₂ = 21 ways
and they can choose 1 floor in 9 ways
now remaining 5 persons and 8 floors
and they can be in ⁸P₅ = 6720 ways
Hence Probability = 21 * 9 * 6720 / 9⁷
= 21 * 6720 / 9⁶
= 21 * 6720 / 9⁵ * 3 * 3
= 7 * 2,240 / 9⁵
= 7 * 7 * 320 / 9⁵
= 7² * 320 / 9⁵
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