First slide

Permutations

Question

If the number of ways in which n different things can be distributed among n persons so that at least one person does not get any thing is 232. Then n is equal to

Moderate

A

3
B

4
C

5
D

None of these

Solution

Total number of ways = nⁿ
Number of ways so that each person gets at least one thing (here exactly one thing) = n!
Given, nⁿ – n! = 232
$\begin{matrix} 1^{1} - 1! = 0, 2^{2} - 2! = 2, 3^{3} - 3! = 21, 4^{4} - 4! = 232 \\ ∴ n = 4 \end{matrix}$

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