eight members of the track team run the 800m race. Trophies are awarded for first, second, and third place. How many ways can three of the track team members when a trophy?
8P3
what does that mean
you clearly need to review permutations and combinations.
8P3 = 8*7*6
Formally, that's 8!/(8-3)!
oh ya sorry that makes sense, I apologize
To determine the number of ways three team members can win a trophy, we can use the concept of combinations.
In this scenario, we have eight team members competing for the trophies in the 800m race. To calculate the number of ways we can select three team members to win, we can use the combination formula:
C(n, r) = n! / (r!(n-r)!),
where n is the total number of options (team members) and r is the number of selections (trophies).
In this case, n = 8 (as there are eight team members) and r = 3 (as we want to select three members for the trophies).
Using the formula, we can calculate the number of ways as follows:
C(8, 3) = 8! / (3!(8-3)!),
= 8! / (3!5!),
= (8 * 7 * 6 * 5!) / (3 * 2 * 1 * 5!),
= (8 * 7 * 6) / (3 * 2 * 1),
= 8 * 7 * 6 / 3 * 2,
= 336.
Therefore, there are 336 different ways that three team members can win the trophies in the 800m race.