Combinatorics Intermediate Challenges-I
Six (distinct) people get into an elevator at the ground floor of a hotel which has 10 upper floors. Assuming each person gets off at a randomly chosen floor, what is the probability that no two people get off at the same floor? Express the probability as a decimal, inputing the first 2 decimal places.
This problem is not original. This problem is part of this set .
The answer is 0.15.
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1 solution
To make sure that no two people gets off at the same floor we need to make sure that they chooses different floor.
There are 10 floors we need to select six of them. after we need to permute the people into those six floors
Hence no of possible ways = 1 0 C 6 × 6 !
Total number of ways = 1 0 6
Hence the answer = 1 0 6 1 0 C 6 × 6 ! = 0 . 1 5 1 2