Q. 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
Explanation
(c)
There are two possible cases
Case I Five 1’s, one 2’s, one 3’s
Number of numbers$= \frac{7!}{5!} = 42$
Case II Four 1’s, three 2’s
Number of numbers$= \frac{7!}{4!3!} = 35$
Total number of numbers $42 + 35 = 77$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.