SOLUTION: Phillip and Angeline are to be seated together with 6 other friends in a row of 8 chairs. The seating arrangement is done by drawing of lots. What is the probability that Phillip

Algebra ->  Probability-and-statistics -> SOLUTION: Phillip and Angeline are to be seated together with 6 other friends in a row of 8 chairs. The seating arrangement is done by drawing of lots. What is the probability that Phillip      Log On


   

Question 1153767: Phillip and Angeline are to be seated together with 6 other friends in a
row of 8 chairs. The seating arrangement is done by drawing of lots. What
is the probability that Phillip and Angeline will sit together?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52772) About Me  (Show Source):
You can put this solution on YOUR website!
.

As a first approach, we can consider A and P as one glued object.


Then we have 8-1 = 7 objects, in all (instead of 8 persons).


For these 7 objects, we have 7! of all possible permutations.


More precisely, since the glued object can be in each of the two states, AP and PA, we have, actually, 
2*7! of all possible favorable permutations.


The whole number of all permutations of 8 objects is 8!.


Therefore, the probability under the question is


    P = favored%2Ftotal = %282%2A7%21%29%2F8%21 = 2%2F8 = 1%2F4.    ANSWER

Solved.


Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


If the first of those two is seated in either the first or last seats, then there is only one seat the other can sit in for them to be together.

P(sit together if first one sits in either end seat) = (2/8)(1/7) = 2/56.

If the first one of them sits in any of the other 6 seats, then there are two seats the other can sit in for them to be together.

P(sit together if first one does not sit in either end seat) = (6/8)(2/7) = 12/56.

P(sit together) = 2/56 + 12/56 = 14/56 = 1/4.

Comparing this to the solution by tutor @ikleyn, it is nice to see that two very different but both very logical paths can lead to the solution....