Three persons enter a railway compartment. If there are 5 seats vacant,
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 $={ }^{5} C_{3} \times 3 !=10 \times 6=60$