How many numbers of 6 digits are possible with the property that the sum of their digits is 5?
(A) 96
(B) 104
(C) 120
(D) 126
Answer: (D)
Explanation: There are 6 digits and their sum is 5. So,
a + b + c + d + e + f = 5
where,
1 ≤ a ≤ 9, and 0 ≤ b, c, d, e, f ≤ 9
Therefore,
(a'+1) + b + c + d + e + f = 5 a' + b + c + d + e + f = 4
Hence,
(4+5)C5 = 9C5 = 126
So, option (D) is correct.
Refer method-2: Indistinguishable balls and Distinguishable boxes .
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