The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1,2…
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
55
66
77
88
Solution
There are two possible cases arise:
Case I Five 1's, one 2's, one 3's
$\therefore$ Number of numbers $=\frac{7 !}{5 !}=42$
Case II Four 1's, three 2's
$\therefore$ Number of numbers $=\frac{7 !}{4 ! 3 !}=35$
$\therefore$ Total number of numbers $=42+35=77$