SOLUTION: April, Bill, Carl, and Denise are to be seated at random in a row of four chairs. What is the probability that April and Bill will occupy the end seats?

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Question 1157465: April, Bill, Carl, and Denise are to be seated at random in a row of four chairs. What is the probability that April and Bill will occupy the end seats?
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
These are all possible seating arrangements with A and B in the end seats:

{ACDB,ADCB,BCDA,BDCA}

That's 4 ways out of 4!=24.

So the probability is 4/24 which reduces to 1/6.

Edwin

Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.

The number of all possible permutations of 4 persons is 4! = 4*3*2*1 = 24.


The number of all possible arrangements, where A an B occupy the end seats is 2*2 = 4

(two positions for A abd B;  and two positions for C and D).


Therefore, the probability is  P = 4%2F24 = 1%2F6.

Solved.