Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is [2023]

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Solution

Q.
Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is [2023]

1 3360

2 1120

3 1680

4 560

Ans.
(3)

8 persons can be divided into 3 groups of 3, 3, and 2 members each.

$∴$ $Required number of ways = \frac{8!}{3! 3! 2! 3!} \times 3!$

$= \frac{8 \times 7 \times 6 \times 5 \times 4}{4} = 56 \times 30 = 1680$

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