Question

7) (a) (2 pts) How many permutations are there of the word QUARANTINE?

(b) (4 pts) How many of the permutations of QUARANTINE do NOT the same letter appearing consecutively? (Thus, any permutation with the substring "AA" should not be counted and any permutation with the substring "NN" should not be counted.)

(c) (6 pts) A mountain permutation is defined as one where the first portion of the permutation has letters in strictly increasing alphabetical order, and the second portion with the letters in strictly decreasing alphabetical order. One mountain permutations of the letters in QUARANTINE is AINTURQNEA. Notice that only a set of letters with a unique "maximum" alphabetic letter have mountain permutations. For this permutation, A < I < N < T < U, and U > R > Q > N > E > A. How many mountain permutations are there of the letters in the word QUARANTINE?

Answer 1