Will decides to attend a basketball game with four friends. If the party of five sits together in five consecutive seats, and Will must NOT sit in between two of his friends, how many ways can the five friends be arranged?
(A) 24
(B) 36
(C) 48
(D) 72
(E) 120
"Will must NOT sit in between two of his friends" means that he must st on ether end o the ve people .e.
1) W _ _ _ _
or
2) _ _ _ _ W
Hence
Case 1) Possibilities at the 5 positions respectively are
\(1 * 4 * 3 * 2 * 1 = 24\)
Since for 2nd position their are four of his friends to sit and anyone can take that place. After that 3rd position has 3 people left to take the place and for 4th position 2 are left and finally last one takes the last place.
Case 2) Possibilities at the 5 positions respectively are
\(4 * 3 * 2 * 1 * 1 = 24\)
Will takes place the fifth position since positions 1, 2, 3 & 4 are not for him as per condition laid out in question.
As explained for case 1 similarly, positions with their respective possibilities are filled up.
Thus, \(24 + 24 = 48\)
Answer (C).
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Ephemeral Epiphany..!
GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019