What is the probability that a randomly chosen positive factor of 6^10 is a multiple of 27?
Solution:
6^10=(2^10)(3^10)
(m+1)(n+1)=11×11= 121 factors
27=3^3
(2^10)(3^10)/3^3=3^7•2^10
3^7•2^10 multiple of 27
(m+1)(n+1)= 8×11= 88
88/121= 8/11
