Question

At a horse show, ribbons are awarded for first, second, third, and fourth places. There are 16 horses in the show. How many different arrangements of four horses are possible?

Answer 1

Answer:

43680 different arrangements are possible.

Step-by-step explanation:

The total number of horses are :16

We have to find different arrangement of four horses

Since, we have to find arrangements means we will use permutation

So, the required arrangement will be:

$^{16}P_4$

Now, using: $^{n}P_r=\frac{n!}{(n-r)!}$

Here, n= 16 and r=4 on substituting the values we get:

$^{16}P_4=\frac{16!}{(16-4)!}$

$\Rightarrow \frac{16!}{12!}$

$\Rightarrow \frac{16\cdot 15\cdot 14\cdot 13\cdot 12!}{12!}$

Cancel out the common term that is 12! we get:

$16\cdot 15\cdot 14\cdot 13$

After simplification we get: 43680

Hence, 43680 different arrangements are possible.