A five-digit number is formed by the digits 1 | vedclass

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(A) The total number of five-digit numbers formed using the digits $1, 2, 3, 4, 5$ without repetition is $5! = 120$. $A$ number is divisible by $4$ if

Vedclass · Accepted Answer

$\frac{1}{5}$

Vedclass · Answer

(A) The total number of five-digit numbers formed using the digits $1, 2, 3, 4, 5$ without repetition is $5! = 120$. $A$ number is divisible by $4$ if its last two digits form a number divisible by $4$. Using the digits ${1, 2, 3, 4, 5}$,the possible two-digit combinations divisible by $4$ are $12, 24, 32, 52$. For each of these $4$ cases,the remaining $3$ digits can be arranged in the first $3$ positions in $3! = 6$ ways. Thus,the total number of favorable outcomes is $4 	imes 3! = 4 	imes 6 = 24$. The required probability is $\frac{24}{120} = \frac{1}{5}$.

$A$ five-digit number is formed by the digits $1, 2, 3, 4, 5$ with no digit being repeated. The probability that the number is divisible by $4$ is

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