(D) To form a number strictly between $5000$ and $10000$,the number must be a $4$-digit number.The first digit (thousands place) must be greater than

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(D) To form a number strictly between $5000$ and $10000$,the number must be a $4$-digit number.The first digit (thousands place) must be greater than or equal to $5$. Given the set of digits $\{1, 3, 5, 7, 9\}$,the possible choices for the thousands place are $5, 7, 9$ ($3$ choices).Since repetition is not allowed,we have $4$ remaining digits for the hundreds place,$3$ remaining digits for the tens place,and $2$ remaining digits for the units place.Total numbers $= 3 \times 4 \times 3 \times 2 = 72$.

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

Medium

The number of numbers,strictly between $5000$ and $10000$,that can be formed using the digits $1, 3, 5, 7, 9$ without repetition is $..........$.

JEE MAIN 2023 All JEE MAIN

A
$6$
B
$12$
C
$120$
D
$72$

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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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The number of numbers,strictly between $5000$ and $10000$,that can be formed using the digits $1, 3, 5, 7, 9$ without repetition is $..........$.

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