Triple Permutation

Calculate the permutations: 5P1 x 10P3 x 4P2

Hint
The number of different permutations of "n" distinct objects taken "r" at a time is:
$$$P_{(n,r)}=\frac{n!}{(n-r)!}$$$
Hint 2
Permutation format: $$nPr$$
The number of different permutations of "n" distinct objects taken "r" at a time is:
$$$P_{(n,r)}=\frac{n!}{(n-r)!}$$$
Solving the first permutation:
$$$P_{(5,1)}=\frac{5!}{(5-1)!}=\frac{5!}{4!}=\frac{5\cdot 4!}{4!}=5$$$
Solving the second permutation:
$$$P_{(10,3)}=\frac{10!}{(10-3)!}=\frac{10!}{7!}=\frac{10\cdot 9 \cdot 8 \cdot 7!}{7!}=720$$$
Solving the third permutation:
$$$P_{(4,2)}=\frac{4!}{(4-2)!}=\frac{4!}{2!}=\frac{4\cdot 3\cdot 2!}{2!}=12$$$
Multiplying the three permutations together:
$$$5 \times 720 \times 12=43,200$$$
43,200