Five balls of different colors are to be plac | vedclass

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

Question

(A) Let the number of balls in the three boxes be $(n_1, n_2, n_3)$ such that $n_1 + n_2 + n_3 = 5$ and $n_i \ge 1$.The possible partitions of $5$ int

Vedclass · Accepted Answer

$150$

Vedclass · Answer

(A) Let the number of balls in the three boxes be $(n_1, n_2, n_3)$ such that $n_1 + n_2 + n_3 = 5$ and $n_i \ge 1$.The possible partitions of $5$ into $3$ parts are $(3, 1, 1)$ and $(2, 2, 1)$.Case $1$: Partition $(3, 1, 1)$.The number of ways to distribute the balls is $\frac{5!}{3!1!1!} 	imes \frac{3!}{2!} = 20 	imes 3 = 60$.Case $2$: Partition $(2, 2, 1)$.The number of ways to distribute the balls is $\frac{5!}{2!2!1!} 	imes \frac{3!}{2!} = 30 	imes 3 = 90$.Total number of ways = $60 + 90 = 150$.

Five balls of different colors are to be placed in three boxes of different sizes,where each box can hold all five balls. In how many ways can the balls be placed such that no box remains empty?

Similar Questions

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

The number of three-digit numbers in which $9$ appears in exactly one place is

If $\alpha = ^mC_2$,then $^\alpha C_2$ is equal to

Consider the following two statements:
$I.$ If $n$ is a composite number,then $n$ divides $(n-1)!$.
$II.$ There are infinitely many natural numbers $n$ such that $n^3+2n^2+n$ divides $n!$.

For $n \geq 2$,let $S_n$ denote the set of all subsets of $\{1, 2, \ldots, n\}$ such that no two elements are consecutive. For example,$\{1, 3, 5\} \in S_6$,but $\{1, 2, 4\} \notin S_6$. Then $n(S_5)$ is equal to . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module