Question

In the decimal system of numeration the number of 6-digit numbers in which the digit in any place is greater than the digit to the left of it is

• A. 210
• B. 84
• C. 126
• D. none of these

Answer 1

The correct option is B 84

Given, 6- digit numbers in which the digit in any place is greater than the digit to the left of it
So, this can be same as selecting $6$ numbers from $1$ to $9$ ($0$ is excluded because if zero is selected, that makes it the least and should be paced at the first place that makes it a $5$ digit number)
i.e. ${}^n{\text{C}}_r$
${=}^9{\text{C}}_6$
$=84$