How many five-digit numbers can be formed usi | vedclass

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(A) The given digits are $2, 0, 4, 3, 8$. To form a five-digit number,the first digit (ten-thousands place) cannot be $0$. Total permutations of $5$ d

Vedclass · Accepted Answer

$96$

Vedclass · Answer

(A) The given digits are $2, 0, 4, 3, 8$. To form a five-digit number,the first digit (ten-thousands place) cannot be $0$. Total permutations of $5$ distinct digits is $5! = 120$. Numbers starting with $0$ are those where the first position is fixed as $0$,and the remaining $4$ positions are filled by the remaining $4$ digits in $4!$ ways. $4! = 24$. Therefore,the number of five-digit numbers = (Total permutations) - (Numbers starting with $0$) $= 5! - 4! = 120 - 24 = 96$.

How many five-digit numbers can be formed using the digits $2, 0, 4, 3, 8$ if repetition of digits is not allowed?

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