Question

question 2
to choose the three players fairly, coach bennet decides to set up a free throw contest. the three players who make the most consecutive free throws will get to go to the summer basketball clinic.
part a
how many different orders of top - three finishers are possible?
drag the tiles to the correct locations on the equation. not all tiles will be used.
permutation formula box = numerator box/denominator box = result box
tiles: 2,184, 3!11!, p, 11!, 14!, c, 364

Explanation:

Step1: Identify permutation type

We need ordered top 3 finishers, so use permutation formula $_nP_r = \frac{n!}{(n-r)!}$. Assume total players $n=14$ (from tile 14!), $r=3$.

Step2: Fill permutation notation

$_nP_r$ becomes $_{14}P_3$, so first blank is $P$.

Step3: Write permutation formula

Substitute $n=14, r=3$: $\frac{14!}{(14-3)!} = \frac{14!}{11!}$

Step4: Calculate the value

$\frac{14!}{11!}=14\times13\times12=2184$

Answer:

First blank (between $n$ and $r$): $P$
Numerator of the fraction: $14!$
Denominator of the fraction: $11!$
Final result blank: $2,184$

Filled equation: $_{14}P_3 = \frac{14!}{11!} = 2,184$