Question

If you are the owner of a NASCAR organization with four racing teams. For each team, it has one primary car and one backup car. You have six haulers in the shop, and each hauler has 2 car bays. You need to select 4 haulers and put those 8 race cars into them.

(a) How many possible assignments could you have?

(b) How many possible assignments if the cars from the same team must be in the same hauler?

Answer 1

Please note

_______________________________________

(a) We select 4 haulers out of 6 in 6C4 ways = 15 ways

There are 8 slots, into which 8 cars have to go, and they can go in 8! ways = 40320 ways

Therefore Total Possible Assignments = 15 * 40320 = 604,800 assignments

_______________________________________

(b) We select 4 haulers out of 6 in 6C4 ways = 15 ways

The teams of cars can be arranged in 4! ways in the 4 haulers = 24

Each hauler can rearrange the 2 cars in 2! = 2 ways

Therefore the Total number of assignments = 15 * 24 * 2 = 720 assignments

__________________________________________