How many ways can the top 5 teams be arranged in a league containing 21 teams? I'm not sure if this is permutation or combination. I think its combination, am I right?
Never mind, its permutation because it's the top 5 teams, right?
I agree, it is a permutation.
It's a permutation because you care about how they are ordered, not because they are the top five teams.
To determine the number of ways the top 5 teams can be arranged in a league containing 21 teams, we need to use permutations, not combinations. Permutations are used when order matters, while combinations are used when order does not matter.
In this case, the order of the top 5 teams does matter since the arrangement will affect their positions in the league. Therefore, we need to use permutations.
The formula for permutations is given by:
P(n, r) = n! / (n - r)!
where n is the total number of objects and r is the number of objects selected.
In this case, we want to find the number of ways to arrange 5 teams out of a total of 21 teams. So, the calculation is P(21, 5) which is:
P(21, 5) = 21! / (21 - 5)!
= 21! / 16!
= (21 * 20 * 19 * 18 * 17 * 16!) / 16!
= (21 * 20 * 19 * 18 * 17)
= 1,270,560
Therefore, there are 1,270,560 ways to arrange the top 5 teams in a league containing 21 teams.