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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 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. −|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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