The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

Options

A. 55
B. 66
C. 77
D. 88

Answer

C

Explanation

Coefficient of `x^(10)(x+x^(2)+x^(3))^(7)`
`implies` Coefficient of `x^(3)` in `(1+x+x^(2))^(7)`
`implies`Coefficient of `x^(3)` in `((1-x^(3))/(1-x))^(7)=(1-x^(3))^(7)(1-x)^(-7)`
`implies`Coefficient of `x^(3)`in `(1-7x^(3))(1+.^(7)C_(1)x+.^(8)C_(2)x^(2)+.^(9)C_(3)x^(3)+ . .. )`
`=.^(9)C_(3)-7=(9*8*7)/(1*2*3)=77`