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(D) To form a number greater than $40000$ using the digits $2, 4, 5, 5, 7$,the first digit must be $4, 5,$ or $7$.Case $1$: If the first digit is $4$,

Vedclass · Accepted Answer

$48$

Vedclass · Answer

(D) To form a number greater than $40000$ using the digits $2, 4, 5, 5, 7$,the first digit must be $4, 5,$ or $7$.Case $1$: If the first digit is $4$,the remaining $4$ digits $(2, 5, 5, 7)$ can be arranged in $\frac{4!}{2!} = \frac{24}{2} = 12$ ways.Case $2$: If the first digit is $5$,the remaining $4$ digits $(2, 4, 5, 7)$ can be arranged in $4! = 24$ ways.Case $3$: If the first digit is $7$,the remaining $4$ digits $(2, 4, 5, 5)$ can be arranged in $\frac{4!}{2!} = \frac{24}{2} = 12$ ways.Total numbers $= 12 + 24 + 12 = 48$.

How many numbers greater than $40000$ can be formed using the digits $2, 4, 5, 5, 7$?

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