Olympiad workbookIOQMPermutation and Combination
Find the number of ordered triples (a, b, c) of positive integers such that a b c=108 .
Correct answer
60
Step-by-step solution
aligned & a b c=3^3 2^2 & a=3^ ₁ 2^ ₁ , b=3^ ₂ 2^ ₂ , c=3^ ₃ 2^ ₃ & ₁+ ₂+ ₃=3 and ₁+ ₂+ ₃=3 & ^5 C₂ and ^4 C₂ & Total = ^4 C₂ ^5 C₂=10 6=60 aligned