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GATE | GATE-CS-2001 | Question 26

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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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