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7) (a) (2 pts) How many permutations are there of the word QUARANTINE? (b) (4 pts) How...

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Advance Math

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

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

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

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