2015 YJC P2 Q9

Five-letter codewords are formed using the letters of the word MATHEMATICS.

1. Find the number of codewords that can be formed if there are no restrictions.[4]
2. Find the probability that a codeword
   1. contains both M’s and both A’s,[1]
   2. has both A’s separated, given that it contains all the four vowels.[3]

TGM probability model for part (b): choose uniformly at random from the distinct five-letter codewords counted in part (a). Each distinct codeword is equally likely.