SOLUTION: (a) in how many ways can the letters of the word be arranged in a line? (b) In how many ways can the arrangement begins with F and ends with 5?

Algebra ->  Permutations -> SOLUTION: (a) in how many ways can the letters of the word be arranged in a line? (b) In how many ways can the arrangement begins with F and ends with 5?      Log On


   

Question 1203275: (a) in how many ways can the letters of the word be arranged in a line?
(b) In how many ways can the arrangement begins with F and ends with 5?
Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


(a) That's 9 different letters; the number of ways of arranging them is 9! = 362880

(b) 0 (there is no "5")

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Part (a)

There are 9 choices in the first slot, then 8 for the next, and so on.

9*8*7*6*5*4*3*2*1 = 362,880 different ways to arrange the letters of FACETIOUS.

For more information, search out "factorial".

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Part (b)

I'm assuming the "5" should be "S"

We have F locked in the first slot and S locked in the last slot.

There are 2 letters locked in place.
That leaves 9-2 = 7 letters left to arrange in 7 slots.

7*6*5*4*3*2*1 = 5,040 different ways to arrange the letters of FACETIOUS such that the "word" begins with F and ends with S.