Bunuel wrote:
How many positive integers less than 10,000 are there in which the sum of the digits equals 5?
(A) 31
(B) 51
(C) 56
(D) 62
(E) 93
positive integers < 10,000… are from 1 to 9999, so we can go from 1-digit number to 4-digitsnumber;
\(x_1+x_2+x_3+x_4=5…(digit.slots)=(sum.five)\)
\(c(n+r-1,r-1)=c(5+4-1,4-1)=c(8,3)=\frac{8!}{3!5!}=\frac{8,7,6}{3,2}=8•7=56\)
Answer (C)
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