In a car race, there are 6 Chevrolets, 4 Fords, and 2 Pontiacs.
In how many ways can the 12 cars finish if we consider
only the makes of the cars?
considering cars, there are 12! ways
now, considering ways..
Ways= 12!/(6!4!2!)
12!/[6!*4!*2!] = (7*8*9*10*11*12)/(2*24)
= 13,860
To calculate the number of ways the 12 cars can finish based on the makes of the cars, we can use the concept of permutations.
First, let's consider the number of ways the Chevrolet cars can finish. Since there are 6 Chevrolets, we can arrange them in 6! (6 factorial) ways.
Next, let's consider the number of ways the Ford cars can finish. Similarly, since there are 4 Fords, we can arrange them in 4! ways.
Lastly, let's consider the number of ways the Pontiac cars can finish. Since there are 2 Pontiacs, we can arrange them in 2! ways.
Now, since the Chevrolet, Ford, and Pontiac cars can finish independently of each other, we multiply the number of arrangements for each make of car.
Therefore, the total number of ways the 12 cars can finish is given by:
Total ways = Number of ways Chevrolet cars can finish * Number of ways Ford cars can finish * Number of ways Pontiac cars can finish
Total ways = 6! * 4! * 2!
Calculating this expression will give us the final answer.