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The number of seven digit integers with ...

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 :

A

55

B

66

C

77

D

88

Text Solution

Verified by Experts

The correct Answer is:
C
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`
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