- #1
pivoxa15
- 2,255
- 1
Homework Statement
Decide in how many ways the letters of the word ABRACADABRA can be arranged in a row if C, R and D are not to be together.
Homework Equations
The number of ways of arranging n objects which include 'a' identical objects of one type, 'b' identical objects of another type,... is
n!/(a!b!...)
n objects divided into m groups with each group having G1, G2, ..., Gm objects respectively has m! * G1! * G2! * ... *Gm!
The Attempt at a Solution
A: 5
B: 2
R: 2
C: 1
D: 1
11 letters in total.
There are a few identical letters so the total number of ways of permuting the objects accounting for the identical letters is 11!/(5!2!2!)
The total number of ways of arranging the letters such that C, R and D are together is:
8!4!/(5!2!2!) as there are 8 groups, with one group containing 4 letters. However given the identical letters, we divide by the same number as above.
So (11!-8!4!)/(5!2!2!)=81144
The answers suggested 78624
I can't see what is wrong with my reasoning.