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GATE | GATE-CS-2001 | Question 26

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  • Last Updated : 28 Jun, 2021
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How many 4-digit even numbers have all 4 digits distinct?
(A) 2240
(B) 2296
(C) 2620
(D) 4536


Answer: (B)

Explanation: This is a basic permutation combination question. Considering two cases :
numbers ending with 0 and not ending with 0: Numbers ending with 0 1{first place: 0} ∗9{fourth place: 9 possibilities, 1-9} ∗8{third place: 8 possibilities left} ∗7{second place: 7 possibilities left} = 504 Numbers ending with non-0 4{first place: 2,4,6,8} ∗8{fourth place: 8 possibilities left, 1-9}∗8{third place: 8 possibilities left b/w 0-9} ∗7{second place: 7 possibilities left b/w 0-9} = 2592
Total = 2296

See https://in.answers.yahoo.com/question/index?qid=20090417083307AA61h9I

This solution is contributed by vineet purswani

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