Question

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

• A. $210$
• B. $240$
• C. $320$
• D. None of the above

Answer 1

The correct option is A $210$

$4$ digits are to be selected from any of $10$ numbers.

Since numbers is in descending order first number can't be till $3.$

The total ways are to select from $0,1,\mathrm{2......9}$

$={}^{10}{C}_4$

and only one way is in descending.

So, total ways ${}^{10}{C}_4.$

$=\frac{10!}{6!4!}$

Hence the answer is $210.$