JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Permutations and Combinations

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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:

(A)3360
(B)1680✓ Correct
(C)560
(D)1120

Answer: (B)

Solution

Seating

8

persons in

3

distinct cars holding at most

3

each forces the size pattern

3, 3, 2

. Choose the car that holds

2

3

ways, pick those

2

persons in

(2 8) = 28

ways, and split the remaining

6

between the two three-seat cars in

(3 6) = 20

ways. The total is

3 \times 28 \times 20 = 1680

JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Single correct option

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