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

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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:

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