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The total number of 4 digit numbers in w...

The total number of 4 digit numbers in which the digit are in descending order, is

A

`""^(10)C_(4)xx4!`

B

`""^(10)C_(4)`

C

`(10!)/(4!)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
The total number of arrangements of 10 digits 0, 1, 2,……,9 by taking 4 at a time `=""^(10)C_(4)xx4!`
We observe that in every arrangement in which the digits are in descending order. Hence,
The required number of numbers `=(""^(10)C_(4)xx4!)/(4!)=""^(10)C_(4)`.
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