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

Options

A. `""^(10)C_(4)xx4!`
B. `""^(10)C_(4)`
C. `(10!)/(4!)`
D. none of these

Answer

B

Explanation

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)`.