The number of four-digit numbers that can be | vedclass

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(B) number is divisible by $4$ if the number formed by its last two digits is divisible by $4$. The available digits are ${1, 2, 3, 4, 5, 6, 7}$.Possi

Vedclass · Accepted Answer

$200$

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(B) number is divisible by $4$ if the number formed by its last two digits is divisible by $4$. The available digits are ${1, 2, 3, 4, 5, 6, 7}$.Possible two-digit combinations (tens,units) divisible by $4$ are: $12, 16, 24, 32, 36, 52, 56, 64, 72, 76$.There are $10$ such pairs.For each pair,we need to fill the remaining $2$ places (thousands and hundreds) using the remaining $5$ digits.The number of ways to fill the remaining $2$ places is $P(5, 2) = 5 	imes 4 = 20$.Total numbers $= 10 	imes 20 = 200$.

The number of four-digit numbers that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ which are divisible by $4$,when the repetition of any digit is not allowed,is:

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