In how many ways can n prizes be distributed | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The total number of ways to distribute $n$ distinct prizes among $n$ boys is $n^n$,as each prize can be given to any of the $n$ boys.There are $n$

Vedclass · Accepted Answer

$n^n - n$

Vedclass · Answer

(C) The total number of ways to distribute $n$ distinct prizes among $n$ boys is $n^n$,as each prize can be given to any of the $n$ boys.There are $n$ cases where a single boy receives all $n$ prizes (i.e.,Boy $1$ gets all,Boy $2$ gets all,...,Boy $n$ gets all).Therefore,the number of ways such that no boy gets all the prizes is the total number of ways minus the cases where one boy gets all prizes.Result $= n^n - n$.

In how many ways can $n$ prizes be distributed among $n$ boys such that no boy gets all the prizes?

Similar Questions

Let $A = \{(a, b, c) : a, b, c \text{ are non-negative integers and } a + b + 2c = 22\}$. Then $n(A)$ is equal to:

Let $n = 1! + 4! + 7! + \ldots + 400!$. Then the ten's digit of $n$ is

Total number of $3$ letter words that can be formed from the letters of the word $'SAHARANPUR'$ is equal to

In an examination,a student has to write exams in $8$ different subjects. He is declared fail if he fails in at least one subject. The number of ways in which he can fail is

The number of three-digit numbers $\overline{abc}$ such that the arithmetic mean of $b$ and $c$ is equal to the square of their geometric mean is

Vedclass Test Series

Exam Paper Generator

Online Exam Module