(A) Since the order of digits matters,we are looking for the number of permutations of $9$ distinct digits taken $4$ at a time.The number of ways to f

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(A) Since the order of digits matters,we are looking for the number of permutations of $9$ distinct digits taken $4$ at a time.The number of ways to form a $4$-digit number is given by the permutation formula $^nP_r = \frac{n!}{(n-r)!}$.Here,$n = 9$ and $r = 4$.Therefore,the number of $4$-digit numbers $= ^9P_4 = \frac{9!}{(9-4)!} = \frac{9!}{5!} = 9 \times 8 \times 7 \times 6 = 3024$.

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

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How many $4$-digit numbers can be formed by using the digits $1$ to $9$ if repetition of digits is not allowed?

A
$3024$
B
$3025$
C
$3026$
D
$3027$

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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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How many $4$-digit numbers can be formed by using the digits $1$ to $9$ if repetition of digits is not allowed?

Similar Questions

How many $8$-digit numbers can be formed such that all digits are distinct?

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The letters of the word $OUGHT$ are written in all possible ways and these words are arranged as in a dictionary,in a series. Then the serial number of the word $TOUGH$ is :

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