(A) The total number of digits is $7$.The digits are $1, 2, 3, 2, 3, 3, 4$.Here,the digit $3$ is repeated $3$ times and the digit $2$ is repeated $2$

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(A) The total number of digits is $7$.The digits are $1, 2, 3, 2, 3, 3, 4$.Here,the digit $3$ is repeated $3$ times and the digit $2$ is repeated $2$ times.The number of distinct permutations is given by the formula $\frac{n!}{p!q!r!...}$.Required number $= \frac{7!}{3! \times 2!} = \frac{5040}{6 \times 2} = \frac{5040}{12} = 420$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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

A
$420$
B
$840$
C
$2520$
D
$5040$

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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Let $P$ be the set of seven-digit numbers with the sum of their digits equal to $11$. If the numbers in $P$ are formed by using the digits $1, 2,$ and $3$ only,then the number of elements in the set $P$ is:

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Let $n$ be a number of digits. Using the three digits $2, 5, 7$,at least $900$ distinct $n$-digit numbers can be formed. What is the minimum value of $n$?

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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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