GATE | GATE-CS-2001 | Question 26
How many 4-digit even numbers have all 4 digits distinct?
(A)
4536
(B)
2620
(C)
2296
(D)
2240
Answer: (C)
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
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Last Updated :
28 Jun, 2021
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