CAT 2021 Slot 3 Quant Question Paper Number System Question

Question of The Day20-02-2023

A four-digit number is formed by using only the digits 1, 2 and 3 such that both 2 and 3 appear at least once. The number of all such four-digit numbers is

Answer

Correct Answer : c ) 50

Explanation :

It is given that

The four-digit number is formed by using the digits 1, 2 and 3 only.

2 and 3 will appear at least once

So, we have to find the number of all such possible numbers.

Here,

Let us calculate the total number of all such possible numbers where we have at least one 2 and one 3

3 x 3 x 3 x 3 = 81

Total number of possible digits with at least one 2 and one 3 = All possible digits - All possible digits with 1 and 2 only - All possible digits with 1 and 3 only -+All possible digits with 1 only ....1

All possible digits with 1 only = 1 x 1 x 1 x 1 = 1

All possible digits with 1 and 2 only = 2 x 2 x 2 x 2 = 16

All possible digits with 1 and 3 only = 2 x 2 x 2 x 2 = 16

Substituting all values in eq. 1

Total number of possible digits with at least one 2 and one 3 = 81 - 16 - 16 + 1 = 50

Hence, the correct answer is c.