JEE MAIN - Mathematics (2023 - 10th April Evening Shift - No. 2)
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 :
560
1680
3360
1120
Explanation
Let $C_1, C_2$ and $C_3$ be the three cars in which 8 person are to be transported from city $A$ to city $B$.
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Let the number of persons transported in cars $C_1, C_2$ and $C_3$ are 3,3 and 2 respectively.
There are total $\frac{8 !}{3 ! 3 ! 2 ! 2 !}$ group
$\therefore$ They can travel $\frac{8 !}{3 ! 3 ! 2 ! 2 !} \times 3$ ! ways or 1680 ways
Let the number of persons transported in cars $C_1, C_2$ and $C_3$ are 3,3 and 2 respectively.
There are total $\frac{8 !}{3 ! 3 ! 2 ! 2 !}$ group
$\therefore$ They can travel $\frac{8 !}{3 ! 3 ! 2 ! 2 !} \times 3$ ! ways or 1680 ways
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