19 cars start a race. in how many ways can the top 3 cars finish
if its permutation its 5,814
or combination its 969
im pretty sure its permutation though
To determine the number of ways the top 3 cars can finish a race with 19 cars, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order.
In this case, we need to find the number of permutations for choosing the top 3 cars from the 19 available. We can calculate this using the formula for permutations:
P(n, r) = n! / (n - r)!
Where "n" is the total number of objects (19 cars) and "r" is the number of objects chosen (3 cars). The exclamation mark (!) denotes factorial, which means multiplying a number by all the whole numbers less than it down to 1.
So, let's plug in the values into the formula:
P(19, 3) = 19! / (19 - 3)!
= 19! / 16!
= (19 * 18 * 17 * 16!)/16!
Simplifying the expression, the (16!) terms cancel out, leaving us with:
P(19, 3) = 19 * 18 * 17
Therefore, the top 3 cars can finish the race in 19 * 18 * 17 = 5,826 different ways.