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Q. Number of five digit integers, with sum of the digits equal to 43 are

Permutations and Combinations

Solution:

Case-1 : Digits being used are $9,9,9,9,7$ then the number of numbers formed $=\frac{5 !}{4 !}=5$
Case-2 : Digits being used are $9,9,9,8,8$ then the number of numbers formed $=\frac{5 !}{3 ! 2 !}=10$
$\therefore$ Total number of such numbers are $10+5=15$