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:
[tex]^{16}P_4[/tex]
Now, using: [tex]^{n}P_r=\frac{n!}{(n-r)!}[/tex]
Here, n= 16 and r=4 on substituting the values we get:
[tex]^{16}P_4=\frac{16!}{(16-4)!}[/tex]
[tex]\Rightarrow \frac{16!}{12!}[/tex]
[tex]\Rightarrow \frac{16\cdot 15\cdot 14\cdot 13\cdot 12!}{12!}[/tex]
Cancel out the common term that is 12! we get:
[tex]16\cdot 15\cdot 14\cdot 13[/tex]
After simplification we get: 43680
Hence, 43680 different arrangements are possible.
