Verified Solution • 2025–26 Session moderate

QJEEM23Mace38: JEE Main 2023 Mathematics - Class 11 JEEM23Mace38 Solution: Eight persons are to be transported from city A to city B in…

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 :

Multiple Choice Options

  • A 560
  • B 1680
  • C 3360
  • D 1120

Step-by-Step Verified Solution

Let C1,C2C_1, C_2 and C3C_3 be the three cars in which 8 person are to be transported from city AA to city BB .

JEE Main 2023 (Online) 10th April Evening Shift Mathematics - Permutations and Combinations Question 45 English Explanation
Let the number of persons transported in cars C1,C2C_1, C_2 and C3C_3 are 3,3 and 2 respectively.

There are total 8!3!3!2!2!\frac{8 !}{3 ! 3 ! 2 ! 2 !} group

∴\therefore They can travel 8!3!3!2!2!×3\frac{8 !}{3 ! 3 ! 2 ! 2 !} \times 3 ! ways or 1680 ways

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