The number of 5-digit numbers which are divis | vedclass

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Question

(A) number is divisible by $4$ if its last two digits are divisible by $4$.Given the set of digits $\{1, 2, 3, 4, 5\}$,the possible two-digit numbers

Vedclass · Accepted Answer

$625$

Vedclass · Answer

(A) number is divisible by $4$ if its last two digits are divisible by $4$.Given the set of digits $\{1, 2, 3, 4, 5\}$,the possible two-digit numbers formed by these digits that are divisible by $4$ are: $12, 24, 32, 44, 52$.There are $5$ such possible combinations for the last two digits.For a $5$-digit number,the first $3$ positions can be filled by any of the $5$ digits because repetition is allowed.Number of ways to fill the first $3$ positions = $5 	imes 5 	imes 5 = 5^3 = 125$.Since there are $5$ possible combinations for the last two digits,the total number of $5$-digit numbers is $125 	imes 5 = 625$.

The number of $5$-digit numbers which are divisible by $4$,with digits from the set $\{1, 2, 3, 4, 5\}$ and the repetition of digits is allowed,is . . . . . .

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