How many numbers lying between 1000 and 10000 | vedclass

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(C) number lying between $1000$ and $10000$ is a $4$-digit number.We have $7$ distinct digits available: ${1, 3, 5, 6, 7, 8, 9}$.Since no digits are r

Vedclass · Accepted Answer

$840$

Vedclass · Answer

(C) number lying between $1000$ and $10000$ is a $4$-digit number.We have $7$ distinct digits available: ${1, 3, 5, 6, 7, 8, 9}$.Since no digits are repeated,we need to arrange $4$ digits out of the $7$ available digits.The number of ways to do this is given by the permutation formula $^nP_r = \frac{n!}{(n-r)!}$.Here,$n = 7$ and $r = 4$.Therefore,the number of ways is $^7P_4 = 7 	imes 6 	imes 5 	imes 4 = 840$.

How many numbers lying between $1000$ and $10000$ can be formed by using the digits $1, 3, 5, 6, 7, 8, 9$ if no digits are repeated?

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