The number of five-digit numbers greater than | vedclass

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(B) To form a five-digit number greater than $50000$ using the digits $0, 1, 3, 5, 9$ exactly once,the first digit (ten-thousands place) must be eithe

Vedclass · Accepted Answer

$48$

Vedclass · Answer

(B) To form a five-digit number greater than $50000$ using the digits $0, 1, 3, 5, 9$ exactly once,the first digit (ten-thousands place) must be either $5$ or $9$.Case $1$: The first digit is $5$.The remaining $4$ digits $(0, 1, 3, 9)$ can be arranged in the remaining $4$ positions in $4! = 4 	imes 3 	imes 2 	imes 1 = 24$ ways.Case $2$: The first digit is $9$.The remaining $4$ digits $(0, 1, 3, 5)$ can be arranged in the remaining $4$ positions in $4! = 4 	imes 3 	imes 2 	imes 1 = 24$ ways.Total numbers $= 24 + 24 = 48$.

The number of five-digit numbers greater than $50000$ that can be formed by using all the digits $0, 1, 3, 5, 9$ only once is

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