please answer question abc l. Now your friend (who lives a little farther from s

Question

please answer question abc l. Now your friend (who lives a little farther from school) wants you to answer the same question for her. Friend's Home School a) How many different possible routes exist if she always travels east or south? b) Could your friend walk to school using a different route every day for an entire term? (Assume a term is 10 weeks long and that she goes to school five days a week for the entire term except for one day which is a holiday.) Explain. IV. How many distinct ways can you rearrange the letters of the following words? a) math b) statistics c) Mississippi d) supercalifragilisticexpialidocious

Explanation / Answer

Ans A). The person would have to walk 6 steps towards right in th east direction(E) and 4 steps in south direction(S) to reach the required destination. Therefore we need to distribute 6 E's and 4 S's.

We can do that like this = 10! / ( 6! X 4!) = 210 ways  

Ans B) . Yes friedn can walk on a different route daily, since the friedn need to tarvel for 50 days ( 10 weeks * 5 days) and we have 210 different shortest routes available

IV)

Permutations of n things of which X1 are alike of one kind, X2 are alike of second kind, X3 are alike of third kind ... Xr are alike of rth kind such that: X1+X2+X3+..+Xr=n is:

n! / X1! * X2! X3!...Xr

Ans a). Rearraggement of Math = 4!

Ans b). Statistics (n=10, 3 S's, 3 t;s, 2 i's) : 10! / 3! * 3! * 2! = 50400

Ans C) . Mississippi ( n= 11, 4 i's, 4 S's, 2 P's) = 11! / ( 4! * 4! * 2!) = 34650

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