(A) Numbers between $5000$ and $10000$ are $4$-digit numbers.The thousands place can be filled by any of the digits from the set $\{5, 6, 7, 8, 9\}$,w

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(A) Numbers between $5000$ and $10000$ are $4$-digit numbers.The thousands place can be filled by any of the digits from the set $\{5, 6, 7, 8, 9\}$,which gives $5$ choices.Since no digit is repeated,we have $8$ remaining digits to fill the remaining $3$ places.The number of ways to fill the remaining $3$ places using $8$ digits is given by $^8P_3$.Therefore,the total number of such numbers is $5 \times ^8P_3$.

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

Medium

How many numbers between $5000$ and $10000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if no digit is repeated?

A
$5 \times ^8P_3$
B
$5 \times ^8C_8$
C
$5! \times ^8P_3$
D
$5! \times ^8C_3$

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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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Medium

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MediumAP EAMCET 2018

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DifficultJEE MAIN 2026

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How many numbers between $5000$ and $10000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if no digit is repeated?

Similar Questions

Find $r$ if $^{5}P_{r} = 2 \times ^{6}P_{r-1}$.

The number of four-letter words that can be formed with letters $a, b, c$ such that all three letters occur is

If the different permutations of all the letters of the word $EXAMINATION$ are listed as in a dictionary,how many words are there in this list before the first word starting with $E$?

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