Question

How many 5 digit even numbers can be made from the digits 1,2,3,4,5 if repetition is not allowed?

• A. 24
• B. 48
• C. 96
• D. 120

Answer 1

The correct option is B

48

Even numbers can be formed by placing either 2 or 4 in the rightmost digit.

_ _ _ _ 2

_ _ _ _ 4

So, let us consider the cases separately.

Case 1: Rightmost digit is 2

_ _ _ _ 2 Available digits 1,3,4,5

Leftmost digit can be filed with 1 or 3 or 4 or 5

So, number if ways of filling leftmost digit = 4

As 2 digits are already used, the next position can be filled with either of the 3 digits.

Proceeding in this manner, the next 2 digits can be filled in 2 and 1 ways respectively.

$\underset{4}{\stackrel{-}{|}}\underset{3}{\stackrel{-}{|}}\underset{2}{\stackrel{-}{|}}\underset{1}{\stackrel{\_2}{|}}$

So, the number of possible numbers = $4\times 3\times 2\times 1$ = 24

Case 2: Rightmost digit is 4

$\underset{4}{\stackrel{-}{|}}\underset{3}{\stackrel{-}{|}}\underset{2}{\stackrel{-}{|}}\underset{1}{\stackrel{\_4}{|}}$

This is similar to case 1.

So, the number of possible numbers = $4\times 3\times 2\times 1$ = 24

$\underset{–}{Conclusion:}$

In total, number of 5 digit even numbers possible = 24 + 24 = 48