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Even 4-digit numbers

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Even 4-digit numbers

by euro » Sun Oct 24, 2010 12:36 am
How many even 4-digit numbers can be formed by using the digits 0-9, so that no two digits are repeated?

(A) 2296
(B) 2396
(C) 2444
(D) 2456
(E) 2486

[spoiler]Don't know the OA. I am getting (A)[/spoiler]
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by shovan85 » Sun Oct 24, 2010 12:59 am
euro wrote:How many even 4-digit numbers can be formed by using the digits 0-9, so that no two digits are repeated?

(A) 2296
(B) 2396
(C) 2444
(D) 2456
(E) 2486

[spoiler]Don't know the OA. I am getting (A)[/spoiler]
Yes indeed U r correct.

ABCD be the 4 digit number

D can be one of (0,2,4,6,8) and ABC cannot be repeated after that.

When D = 0 , A can be chosen in 9 ways, B in 8 and C in 7 ways: Total = 1*9*8*7 = 504
When D = 2 or 4 or 6 or 8 (4 ways)
A can be chosen in 8 ways (as A cannot be zero)
B can be chosen in 8 ways (B can be zero so exclude A only)
C can be chosen in 7 ways (A and B excluded)
Total: 4*8*8*7 = 1792.

Total number of 4 digits numbers = 1792+504 = 2296
If the problem is Easy Respect it, if the problem is tough Attack it
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