In how many ways can 7 different cars be distributed in 5 different showrooms…
2025
In how many ways can 7 different cars be distributed in 5 different showrooms if showroom 3 and showroom 5 can contain only one and two number of cars respectively and rest of the showrooms can contain any number of cars?
Answer: C. 8505 — To solve this, first assign the required number of cars to showroom 3 and showroom 5. Showroom 3 must have exactly one car, so choose 1 out of 7 cars: C(7,1)…
- A.
10100
- B.
6200
- C.
8505
- D.
12800
Attempted by 8 students.
Show answer & explanation
Correct answer: C
To solve this, first assign the required number of cars to showroom 3 and showroom 5.
Showroom 3 must have exactly one car, so choose 1 out of 7 cars: C(7,1) = 7 ways.
Then, showroom 5 must have exactly two cars from the remaining 6: C(6,2) = 15 ways.
The remaining 4 cars can be assigned to any of the other three showrooms (1, 2, and 4), each car having 3 choices.
So the number of ways for these 4 cars is 3^4 = 81. Multiply all together: 7 × 15 × 81 = 8505.