Question
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
Answer :
77
Solution :
We have to form 7 digit numbers, using the digits 1, 2 and 3 only, such that the sum of the digits in a number = 10.
This can be done by taking 2, 2 , 2, 1, 1, 1, 1, or by taking 2,3,1,1,1,1,1.
∴ Number of ways $$ = \frac{{7!}}{{3!4!}} + \frac{{7!}}{{5!}} = 77.$$