First slide

Combinations

Question

$\sum_{r = 0}^{n} \frac{^{n} P_{r}}{r!}$ is equal to

Easy

A

$2^{n - 1}$
B

$2^{n}$
C

$2^{n} + 1$
D

$2^{n - 2}$

Solution

$\sum_{r = 0}^{n} \frac{^{n} p_{r}}{r!} = \sum_{r = 0}^{n}^{n} c_{r} = 2^{n}$

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