Combination
Calculate the combinations: 10C4 x 6C3
Expand 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
Time Analysis
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