How many ways are there to... (a) arrange the letters of the word ALGORITHM in a row? (b) arrange 4 different letters of the word ALGORITHM in a row? (e) arrange the letters of the word ALGORITHM in a row such that all the vowels (A, O, 1) come before all the consonants (L,G, R, T, H, M)? (d) choose 5 different letters from the word ALGORITHM but without arranging them in any order? (e) choose 5 letters from the word ALGORITHM, possibly with repeats, and without arranging them in any order? (f) arrange the letters of the word MATHEMATICIAN in a row? (Watch out for repeats!)