Permutations

#133 / Prob & Stats Medium

Calculate the permutations: 4P2 x 6P3

Expand 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:

$$$P_{(4,2)}=\frac{4!}{(4-2)!}=\frac{4!}{2!}=\frac{4\cdot 3\cdot 2!}{2!}=12$$$

Solving the second permutation:

$$$P_{(6,3)}=\frac{6!}{(6-3)!}=\frac{6!}{3!}=\frac{6\cdot 5\cdot 4\cdot 3!}{3!}=120$$$

Multiplying the two permutations together:

$$$12\times 120=1,440$$$

1,440

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