How many 5-digit numbers can be formed using | vedclass

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Question

(A) The available digits are ${0, 1, 2, 3, 5, 7}$. $A$ $5$-digit number cannot start with $0$.Numbers starting with $1$: $5 	imes 4 	imes 3 	imes 2

Vedclass · Accepted Answer

$500$

Vedclass · Answer

(A) The available digits are ${0, 1, 2, 3, 5, 7}$. $A$ $5$-digit number cannot start with $0$.Numbers starting with $1$: $5 	imes 4 	imes 3 	imes 2 = 120$.Numbers starting with $2$: $5 	imes 4 	imes 3 	imes 2 = 120$.Numbers starting with $3$: $5 	imes 4 	imes 3 	imes 2 = 120$.Numbers starting with $5$: $5 	imes 4 	imes 3 	imes 2 = 120$.Total numbers starting with $1, 2, 3, 5$ is $120 	imes 4 = 480$.Now,consider numbers starting with $7$:$70123, 70125, 70132, 70135, 70152, 70153, 70213, 70215, 70231, 70235, 70251, 70253, 70312, 70315, 70321, 70325, 70351, 70352, 70512, 70513$.Counting these,we find $70513$ is the $20$th number starting with $7$.Rank $= 480 + 20 = 500$.

How many $5$-digit numbers can be formed using the digits $0, 1, 2, 3, 5, 7$ without repetition? If all such numbers are arranged in ascending order,what is the rank of the number $70513$?

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