CPS 341 HOMEWORK 6 Due at class time, in class, Tuesday, 10 April, 2018. NOTE: (

Question

CPS 341 HOMEWORK 6 Due at class time, in class, Tuesday, 10 April, 2018. NOTE: (1) You must write your solutions properly. Solutions without any ex planation will receive no credit. Exhaustive enumeration is not an acceptable counting technique. (2) If you leave your answers in forms such as C(10, 3) x 4!, that would be Gne (3) In the word MOMMY, all the M's are identical. (4) Recall that "or" means "either... or. or b" (1) Consider distinct permutations of the word MAXIMAL (a) (4 pts) How many are there that begin with M? pHaw yehi wht to each other?

Explanation / Answer

a) Distinct permutation of MAXIMAL begin with M : first position can fill by two ways and rest !6. A and M are repeated twice hence total number of ways are:

[C(2,1)x!6]/( !2x!2)

b) To compute number of permutation in which two M are not together i.e next to each other in following way. compute total number of permutation and subtract permutation in which two M are together.

Total number of permutation:  !7/( !2x!2)

Total number of permutation with two M together is !6/( !2)

number of permutation in which two M are not together is: !7/( !2x!2)- !6/( !2)=5*(!6/( !2x!2))

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