Question 1194073: if the letters A, B, C, D, E and F are randomly arranged, calculate the probability that the letters A and B will be next to each other?
Textbook answer is 1/3.
Can someone help me solve this problem? Thanks.
Answer by ikleyn(52782)   (Show Source):
You can put this solution on YOUR website! .
if the letters A, B, C, D, E and F are randomly arranged, calculate the probability
that the letters A and B will be next to each other?
Textbook answer is 1/3.
Can someone help me solve this problem? Thanks.
~~~~~~~~~~~~~~~
In all, there are 6 letters, A, B, C, D, E and F. The numbers of all possible permutations is 6!.
IF the letters A and B form one block AB, then we have, actually, 5 objects to permute:
4 letters C, D, E anf F plus one block AB.
5 objects can be arranged in 5! different ways.
If the letters A and B form one block BA (in this order !), then another 5! different favorable permutations possible.
Thus the number of all favorable permutations with A and B next to each other is 2*5!.
Now the sought probability is the ratio of these two numbers
P =  =  =  . ANSWER
Solved.
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