Find the Number of Possibilities 52 choose 1

${}_{52}C_{1}$

Evaluate ${}_{52}C_{1}$ using the formula ${}_{n}C_{r} = \frac{n!}{r! (n - r)!}$ .

$\frac{52!}{1! (52 - 1)!}$

Subtract $1$ from $52$ .

$\frac{52!}{1! (51)!}$

Simplify $\frac{52!}{1! (51)!}$ .

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Rewrite $52!$ as $52 \cdot 51!$ .

$\frac{52 \cdot 51!}{1! (51)!}$

Cancel the common factor of $51!$ .

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Cancel the common factor.

$\frac{52 \cdot 51!}{1! (51)!}$

Rewrite the expression.

$\frac{52}{1!}$

Expand $1!$ to $1$ .

$\frac{52}{1}$

Divide $52$ by $1$ .

$52$

Find the Number of Possibilities 52 choose 1

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