SOLUTION: Consider the arrangements of the letters in the word ALGORITME. 1. How many arrangements are there? 2. In how many arrangements do the letters R, I, T, M and E remain togethe

Algebra ->  Probability-and-statistics -> SOLUTION: Consider the arrangements of the letters in the word ALGORITME. 1. How many arrangements are there? 2. In how many arrangements do the letters R, I, T, M and E remain togethe      Log On


   

Question 1170587: Consider the arrangements of the letters in the word ALGORITME.
1. How many arrangements are there?
2. In how many arrangements do the letters R, I, T, M and E remain together in this order?
3. What is the probability that the situation in Question 2 will occur?
Thanks!!
Found 2 solutions by akumpo, ikleyn:
Answer by akumpo(8) About Me  (Show Source):
You can put this solution on YOUR website!
1. The word is 9 letters long so the number of arrangements possible would be 9! (9*8*7*6*5*4*3*2*1) which is 362880
2. If RITME must stay in the order, you have to find the number of arrangements for ALGO. This is because if you were to find the arrangements of ALGOR or anything with the letters of RITME, you would mess up the order. The number of arrangements should be 4! or 24.
3. 24/362880, which simplifies to 1/15120.

Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The response of  @akumpo  to part  (2)  is incorrect. 


In part (2), we consider the letters "RITME" in this order as staying together.


It means that you have 5 objects to permute:


      4 objects are the letters A, L, G and O,  and the 5-th object is this block of letters "RITME" - we consider

      this block as one whole entity.


Therefore, we permute 5 objects and have 120 = 5! = 5*4*3*2*1 permutations (= arrangements).    ANSWER to part (2)




Therefore, the answer to part  (3)  ALSO must be corrected. It is

    P = 5%21%2F9%21 = 1%2F%289%2A8%2A7%2A6%29 = 1%2F3024 = 0.000331.                ANSWER to part (3)

Solved.