Question

If 42 people run a race, how many possible sequences are there for the top 5 finishers? (1st, 2nd, 3rd...)

Answer 1

102080160 ways

Explanation:

There are a total of 42 people that participate in a race. We're looking for the top 5 finishers. Therefore, we will use permutation to pick five finishers and arrange them in positions.

`\displaystyle{_n \text{P} _r = (n!)/(\left(n-r\right)!)}`

"n" is the total which is 42, and "r" is the chosen, which is 5. Therefore, substitute in:

`\displaystyle{_(42) \text{P} _5 = (42!)/(\left(42-5\right)!)}\\\\\displaystyle{_(42) \text{P} _5 = (42!)/(37!)}\\\\\displaystyle{_(42) \text{P} _5 = (42 *41 * 40 * 39 * 38 * 37!)/(37!)}\\\\\displaystyle{_(42) \text{P} _5 = 42* 41 * 40 * 39 * 38}\\\\\displaystyle{_(42) \text{P} _5 = 102080160}`

Therefore, 102080160 sequences for the top 5 finishers with 42 participants are possible.