Triple Permutation

#389 / Prob & Stats Medium

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

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:

$$$P_{(5,1)}=\frac{5!}{(5-1)!}=\frac{5!}{4!}=\frac{5\cdot 4!}{4!}=5$$$

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

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