Question

Nia picks five bits of papers from a jar with the numbers 2, 3, 5, 7, and 9 written on them.
Find the number of ways in which Nia can form even 3-digit numbers without repeating them.

• A. 60
• B. 12
• C. 20
• D. 10

Answer 1

The correct option is B 12

The numbers on the papers are 2, 3, 5, 7, and 9.

For a number to be an even number, the units digit should be 0, 2, 4, 6, or 8.

Here, the digit in the ones place of a 3-digit number is 2.


The digit in the tens place can be filled using any number from 3, 5, 7, or 9, except 2.
Let us pick 3 for the tens place.

• Number of ways the tens place can be filled = 4

The digit in the hundreds place can be filled using the remaining three numbers depending on the tens digit chosen.

Since we have 3 in the tens place, we can fill the hundreds place using 5, 7, or 9.

Let us pick 9 for the hundreds place.

• Number of ways the hundreds place can be filled = 3

Thus, there are 4 ways in which the tens place can be filled and 3 ways to fill the hundreds place.

Total number of ways to make a 3-digit number = $4\times 3=12$

Thus, the number of ways in which even 3-digit numbers can be formed is 12.