Combination

Calculate the combinations: 10C4 x 6C3

Hint
$$$C_{(n,r)}=\frac{P_{(n,r)}}{r!}=\frac{n!}{[r!(n-r)!]}$$$
where $$C_{n,r}$$ is the number of different combinations of $$n$$ distinct objects taken $$r$$ at a time, and $$P$$ is the number of different permutations.
Hint 2
Combination format: $$nCr$$
$$$C_{(n,r)}=\frac{P_{(n,r)}}{r!}=\frac{n!}{[r!(n-r)!]}$$$
where $$C_{n,r}$$ is the number of different combinations of $$n$$ distinct objects taken $$r$$ at a time, and $$P$$ is the number of different permutations.
Solving the first combination:
$$$C_{(10,4)}=\frac{10!}{4![(10-4)!]}=\frac{10!}{4!(6!)}=\frac{10\cdot 9\cdot 8\cdot 7\cdot 6!}{4\cdot 3\cdot 2\cdot 1\cdot (6!)}=\frac{5,040}{24}=210$$$
Solving the second combination:
$$$P_{(6,3)}=\frac{6!}{3![(6-3)!]}=\frac{6!}{3!(3!)}=\frac{6\cdot 5\cdot 4\cdot  3!}{3\cdot 2\cdot 1\cdot 3!}=\frac{120}{6}=20$$$
Multiplying the two combinations together:
$$$210\times 20=4,200$$$
4,200