Let n be the number of different 5-digit numb | vedclass

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(C) number is divisible by $4$ if its last two digits form a number divisible by $4$.Given digits are ${1, 2, 3, 4, 5, 6}$.The possible $2$-digit numb

Vedclass · Accepted Answer

$192$

Vedclass · Answer

(C) number is divisible by $4$ if its last two digits form a number divisible by $4$.Given digits are ${1, 2, 3, 4, 5, 6}$.The possible $2$-digit numbers formed by these digits that are divisible by $4$ are: $12, 16, 24, 32, 36, 52, 56, 64$.There are $8$ such possible pairs for the last two digits.For each pair,we need to fill the remaining $3$ positions using the remaining $4$ digits from the set ${1, 2, 3, 4, 5, 6}$.The number of ways to choose and arrange $3$ digits out of $4$ is given by $P(4, 3) = 4 	imes 3 	imes 2 = 24$.Since there are $8$ such pairs,the total number of $5$-digit numbers $n$ is $8 	imes 24 = 192$.

Let $n$ be the number of different $5$-digit numbers,divisible by $4$,formed with the digits $1, 2, 3, 4, 5,$ and $6$,such that no digit is repeated in the numbers. What is the value of $n$?

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