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+1 vote
19.0k views
in Permutations and combinations by (46.7k points)

The total number of three-digit numbers, the sum of whose digits is even, is equal to

(A) 450 

(B) 350 

(C) 250 

(D) 325

1 Answer

+2 votes
by (52.7k points)
selected by
 
Best answer

Correct option  (A) 450 

Let the three-digits of number n = x1,x2,x3.

Since, x1 + x+ xis even, there are following cases:

(a)  x1,x2,x3 all are even. So

4. 5. 5 = 100 ways

(b)  x1 even and x2 , x3 are odd. So

4. 5. 5 = 100 ways

(c)  x1 odd, x2 even, x3 odd. So

5. 5. 5 = 125 ways

(d)  x1 odd, x2 odd, x3 even. So

5. 5. 5 = 125 ways

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