A) Suppose that a monkey randomly types on a typewriter in the following manner: each time he types a lowercase letter, it is equally likely to be any of the 26 letters of the alphabet, regardless of any letters he has previously typed. Ignoring any numerals, punctuation marks, special symbols, spaces, and uppercase letters that he produces, what is the probability that the first six lowercase letters that he types are, in order, i s m a r t?
B) Suppose that a monkey is given six blocks; one with the letter a on it, one with the letter i on it, one with the letter m on it, one with the letter r on it, one with the letter s on it, and one with the letter t on it. If he randomly orders the blocks from left to right, what is the probability that they appear in the order i s m a r t?
C) Suppose that a monkey is given seven blocks; three with the letter a on them, one with the letter b on it, two with the letter n on them, and one with the letter s on it. If he randomly orders the blocks from left to right, what is the probability that they appear in the order b a n a n a s? (Comment: Don't be concerned with the orientation of the letters on the blocks when the monkey randomly places them; just focus on the order in which the seven letters appear when placed from left to right.)
D) Suppose that a monkey is given a collection of 26 blocks, each with a different letter of the alphabet on it. (So the blocks have the letters a, b, c, ..., y, and z on them.) If the monkey randomly chooses a subset of 6 of the blocks, what is the probability that they are the ones with the letters a, i, m, r, s, and t? (Comment: For this part, the blocks are selected without replacement from the collection of 26 blocks. The order in which the blocks are selected doesn't matter; we're only concerned with which blocks comprise the randomly selected subset.)