n-1 1. A car dealership has 8 different high-end sports cars. (Note: For each qu

Question

n-1 1. A car dealership has 8 different high-end sports cars. (Note: For each question below, leave your answer in terms of a formula.) a) In how many ways can the 8 cars be parked in a parking lot (which consists of 8 side-by-side parking spots)? 12 pts Ans b) In how many ways can the cars be parked in a parking lot (which consists of 8 side-by-side parking spots) if three of them A, B, and C must be parked together (in any order)? [3 pts] Ans: c) If the dealership wanted to distribute the 8 cars among its 11salespersons (to oversee their sale) in such a way that no salesperson was to be assigned more than one car, how many possible distributions would there be? (Note that each car is distinct.) [3 pts]

Explanation / Answer

a) since there are 8 spots and 8 cars

We can arrange 8 things in 8 places in 8! ways

b) There must be parked together

Let these three make 1 unit, now we have 5 + 1 units ( 5 cars plus ABC)

So, these can be arranged in 6! ways

Also, ABC can be arranged among themselves in 3! ways

Total = 6! * 3!

c) nCk * r^n

11C8 * 8^8

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