WBJEE · Maths · Permutation Combination
\(\mathrm{n}\) objects are distributed at random among \(\mathrm{n}\) persons. The number of ways in which this can be done so that at least one of them will not get any object is
- A \(n !-n\)
- B \(n^n-n\)
- C \(n^n-n^2\)
- D \(n^n-n\) !
Answer & Solution
Correct Answer
(D) \(n^n-n\) !
Step-by-step Solution
Detailed explanation
Hint : Total number of ways of distributing \(n\) objects randomly among \(n\) persons \(=\mathrm{n}^n\) Number of ways in which each person gets exactly one object \(={ }^n P_n=n\) ! \(\therefore\) Required number of ways \(=n^n-n\) !
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