Expert: Paul Klarreich - 11/19/2008

Question
All letters of the word WARRAGAMBA will be arranged on a line. In how many ways can this be done if
i) letter B comes before letter G
ii)the same letter will appear at both ends

Answer
Questioner:   Verena
Category:  Advanced Math
Private:  No
 
Subject:  Maths
Question:  All letters of the word WARRAGAMBA will be arranged on a line. In how many ways can this be done if
i) letter B comes before letter G
ii)the same letter will appear at both ends
.....................
Hi, Verena,

You should have learned this rule:

Permutations(10 objects, (with 4A,2R)) = 10!/(4!2!)

1) In half of them, B will come before G.
2) If the first and last are A, delete 2A, and do P(8, (2,2)) PLUS
  If the first and last are R, delete 2R, and do P(8, (4))

That should do it.  If you are stuck, send me what you did and what you are studying and I'll see what I can do.