There are 14 NBA teams who do not make
the playoffs. Of these teams, 3 of them will
be randomly selected to make the 1st, 2nd,
and 3rd pick. How many different ways
can the 1st-3rd pick be arranged?
14P3
To find the number of different ways the 1st-3rd pick can be arranged, we can use the concept of permutations. A permutation is an arrangement of objects where the order matters.
In this case, we have 14 teams, and we need to select 3 of them for the 1st, 2nd, and 3rd picks. Therefore, we want to calculate the number of permutations of 14 objects taken 3 at a time.
The formula for permutations is given by:
P(n, r) = n! / (n - r)!
Where n represents the total number of objects and r represents the number of objects chosen.
Applying this formula, we have:
P(14, 3) = 14! / (14 - 3)!
= 14! / 11!
Simplifying further:
14! / 11! = 14 × 13 × 12
= 2184
Therefore, there are 2,184 different ways the 1st-3rd pick can be arranged from the 14 NBA teams that do not make the playoffs.