Number theory question useful for your interviews purpose

[Balaji]

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

Solution

in this sum two cases arises they are

case - 1

7! / 5! = 7 * 6 = 42

case -2

7! / ( 3! * 4! ) = 35

hence the required no of 7 digit numbers is 42 + 35 = 77

so the choice c is correct  answer