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

Answer 1

(a) 60
Three persons can take 5 seats in ⁵C₃ ways. Moreover, 3 persons can sit in $3!$ ways.
∴ Required number of ways = ${}^5{C}_3\times 3!=10\times 6=60$