The number of 7-digit numbers which can be fo | vedclass

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

Question

(A) The given digits are $1, 2, 3, 2, 3, 3, 4$. The total number of digits is $n = 7$.In these digits,the digit $3$ is repeated $3$ times and the digi

Vedclass · Accepted Answer

$420$

Vedclass · Answer

(A) The given digits are $1, 2, 3, 2, 3, 3, 4$. The total number of digits is $n = 7$.In these digits,the digit $3$ is repeated $3$ times and the digit $2$ is repeated $2$ times.The number of distinct permutations of $n$ objects where $n_1$ are of one type,$n_2$ are of another type,etc.,is given by $\frac{n!}{n_1! n_2! \dots}$.Here,$n = 7$,$n_1 = 3$ (for digit $3$),and $n_2 = 2$ (for digit $2$).Required number of $7$-digit numbers = $\frac{7!}{3! 	imes 2!} = \frac{5040}{6 	imes 2} = \frac{5040}{12} = 420$.

The number of $7$-digit numbers which can be formed using the digits $1, 2, 3, 2, 3, 3, 4$ is:

Similar Questions

$A$ committee of $11$ members is to be formed from $8$ men and $5$ women. If $m$ is the number of ways to form the committee with at least $6$ men and $n$ is the number of ways to form the committee with at least $3$ women,then:

If the number of five-digit numbers with distinct digits and $2$ at the $10^{\text{th}}$ place is $336k$,then $k$ is equal to

In how many different ways can the letters of the word '$PRAISE$' be arranged?

Let $A$ and $B$ be two sets containing $4$ and $2$ elements respectively. Then the number of subsets of the set $A \times B$,each having at least $3$ elements is:

The number of ways of selecting $15$ teams from $15$ men and $15$ women,such that each team consists of a man and a woman,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module