Question

How many numbers less than 10000 are there whose sum of the digits is less than or equal to 5?

• A. 192
• B. 100
• C. 126
• D. 189

Answer 1

The correct option is C 126

Let the required number be represented as ABCD.

$A+B+C+D\le 5$

Introducing a dummy variable E,

$A+B+C+D+E=5$

This is the arrangement of 5 zeroes and 4 ones (the number of plus signs). Answer is ${}^9{C}_4=126$.