(A) number is divisible by $4$ if the number formed by its last two digits is divisible by $4$. Using the digits ${1, 2, 3, 4, 5}$,the possible $2$-di

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(A) number is divisible by $4$ if the number formed by its last two digits is divisible by $4$. Using the digits ${1, 2, 3, 4, 5}$,the possible $2$-digit numbers divisible by $4$ are: $12, 24, 32, 52$. There are $4$ such pairs. For each pair,the remaining $3$ positions can be filled by the remaining $3$ digits in $3! = 6$ ways. Total numbers = $(\text{Number of pairs}) \times (3!) = 4 \times 6 = 24$.

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

Medium

How many $5$-digit numbers can be formed using the digits $1, 2, 3, 4, 5$ such that the number is divisible by $4$?

A
$24$
B
$120$
C
$72$
D
None of these

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Permutation and Combination

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

The number of integers between $2,000$ and $5,000$ that can be formed using the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) such that the number is a multiple of $3$ is:

DifficultJEE MAIN 2018

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$a, b, c$ are three particular speakers among the $10$ speakers of a meeting. The number of ways of arranging all the $10$ speakers on the dais in a row so that all the three speakers $a, b, c$ do not sit together is

EasyTS EAMCET 2022

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How many numbers can be formed using the digits $0, 1, 2, 3, 4, 5$ that are greater than $3000$ (repetition is not allowed)?

MediumIIT 1976

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In how many ways can $6$ examination papers be arranged so that the best and the worst papers are never together?

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How many words can be formed from the letters of the word $COURTESY$,whose first letter is $C$ and the last letter is $Y$?

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How many $5$-digit numbers can be formed using the digits $1, 2, 3, 4, 5$ such that the number is divisible by $4$?

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The number of integers between $2,000$ and $5,000$ that can be formed using the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) such that the number is a multiple of $3$ is:

$a, b, c$ are three particular speakers among the $10$ speakers of a meeting. The number of ways of arranging all the $10$ speakers on the dais in a row so that all the three speakers $a, b, c$ do not sit together is

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