If the digits are not allowed to repeat in an | vedclass

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(D) We need to form numbers greater than $10,000$ using the digits $\{0, 2, 4, 6, 8\}$ without repetition. Since we have $5$ distinct digits,any numbe

Vedclass · Accepted Answer

$96$

Vedclass · Answer

(D) We need to form numbers greater than $10,000$ using the digits $\{0, 2, 4, 6, 8\}$ without repetition. Since we have $5$ distinct digits,any number greater than $10,000$ must be a $5$-digit number.For a $5$-digit number,the first digit (ten-thousands place) cannot be $0$. Thus,the first digit can be chosen from $\{2, 4, 6, 8\}$,which gives $4$ choices.The remaining $4$ positions can be filled by the remaining $4$ digits in $P(4, 4) = 4 	imes 3 	imes 2 	imes 1 = 24$ ways.Therefore,the total number of such numbers is $4 	imes 24 = 96$.

If the digits are not allowed to repeat in any number formed by using the digits $0, 2, 4, 6, 8$,then the number of all numbers greater than $10,000$ is equal to $....$

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