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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

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:

Choose the correct answer:

A.
1120
B.
560
C.
3360
D.
1680
(Correct Answer)

Correct Answer:

1680

Explanation

Grouping and Distribution Formula:

\text{Total ways} = \frac{8!}{3! \cdot 3! \cdot 2!} \times \frac{3!}{2!}

2. Step-by-Step Calculation:

\text{Total ways} = \frac{40320}{(6 \times 6 \times 2)} \times 3

\text{Total ways} = \frac{40320}{72} \times 3

\text{Total ways} = 560 \times 3 = 1680

Explanation

Grouping and Distribution Formula:

\text{Total ways} = \frac{8!}{3! \cdot 3! \cdot 2!} \times \frac{3!}{2!}

2. Step-by-Step Calculation:

\text{Total ways} = \frac{40320}{(6 \times 6 \times 2)} \times 3

\text{Total ways} = \frac{40320}{72} \times 3

\text{Total ways} = 560 \times 3 = 1680

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