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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

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B

48

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C

96

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D

120

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Solution

The correct option is C

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.

|4|3|2_2|1

So, the number of possible numbers = 4×3×2×1 = 24

Case 2: Rightmost digit is 4

|4|3|2_4|1

This is similar to case 1.

So, the number of possible numbers = 4×3×2×1 = 24

Conclusion:––––––––––––

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


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