A five-digit number is formed using the digit | vedclass

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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 two-d

Vedclass · Accepted Answer

$\frac{1}{5}$

Vedclass · Answer

(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 two-digit combinations divisible by $4$ are $12, 24, 32, 52$. There are $4$ such favorable combinations for the last two digits. The remaining $3$ positions can be filled by the remaining $3$ digits in $3!$ ways. Total number of favorable outcomes $= 4 	imes 3!$. Total number of possible five-digit numbers $= 5!$. Probability $= \frac{4 	imes 3!}{5!} = \frac{4 	imes 3!}{5 	imes 4 	imes 3!} = \frac{1}{5}$.

$A$ five-digit number is formed using the digits $1, 2, 3, 4, 5$ without repetition. What is the probability that the number is divisible by $4$?

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