# 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

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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

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verified

The correct answer is option C) 77

solution::

there can be two cases

numbers can be

case 1 ::  1, 1, 1, 1, 2, 2, 2

possible 7 digits number by this =$${7!\over 3!4!}=35$$

case 2:: 1, 1, 1, 1, 1, 2, 3

possible 7 digits number by this =$${7!\over 5!}=42$$

Total number of seven digit numbers whose sum is 10 using numbers 1, 2, 3 is 35 + 42 = 77