How many numbers between 5000 and 10,000 can be formed using digits 1, 2, 3, 4, 5, 6, 7, 8, 9 each d

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6.Permutation and Combination

medium

How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ each digit appearing not more than once in each number

A

$5{ \times ^8}{P_3}$

B

$5{ \times ^8}{C_3}$

C

$5\;!\;{ \times ^8}{P_3}$

D

$5\;!\;{ \times ^8}{C_3}$

Solution

(a) A number between $5000$ and $10,000$ can have any of the digits $5, 6, 7, 8, 9$ at thousand's place.

So thousand's place can be filled in $5$ ways.

Remaining $3$ places can be filled by the remaining $8$ digits in $^8{P_3}$ ways

. Hence required number = $5{ \times ^8}{P_3}$.

Standard 11

Mathematics

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