Question:
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
(a) 60
(b) 20
(c) 15
(d) 125
Solution:
(a) 60
Three persons can take 5 seats in 5C3 ways. Moreover, 3 persons can sit in 3! ways.
$\therefore$ Required number of ways $={ }^{5} C_{3} \times 3 !=10 \times 6=60$
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