Question

Paul has 9 soccer trophies, but only 6 will fit on his shelf. In how many different ways can he arrange 6 of the trophies on his shelf?

Answer 1

Answer:

60,480

Step-by-step explanation:

To find the number of ways that Paul can arrange his trophies, we can use the permutation formula.

The permutation formula is:

$_{n}P_{k}=\dfrac{n!}{(n-k)!}$

n = 9

k = 6

Now let's put them into the formula.

$_{9}P_{6}=\dfrac{9!}{(9-6)!}$

$_{9}P_{6}=\dfrac{9!}{3!}$

$_{9}P_{6}=\dfrac{9!}{3!}$

$_{9}P_{6}=60,480$

There are 60,480 different ways that Paul can arrange his trophies on the shelf.