Find the Number of Possibilities 58 choose 6

${}_{58}C_{6}$

Evaluate ${}_{58}C_{6}$ using the formula ${}_{n}C_{r} = \frac{n!}{r! (n - r)!}$ .

$\frac{58!}{6! (58 - 6)!}$

Subtract $6$ from $58$ .

$\frac{58!}{6! (52)!}$

Simplify $\frac{58!}{6! (52)!}$ .

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Rewrite $58!$ as $58 \cdot 57 \cdot 56 \cdot 55 \cdot 54 \cdot 53 \cdot 52!$ .

$\frac{58 \cdot 57 \cdot 56 \cdot 55 \cdot 54 \cdot 53 \cdot 52!}{6! (52)!}$

Cancel the common factor of $52!$ .

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Cancel the common factor.

$\frac{58 \cdot 57 \cdot 56 \cdot 55 \cdot 54 \cdot 53 \cdot 52!}{6! (52)!}$

Rewrite the expression.

$\frac{58 \cdot 57 \cdot 56 \cdot 55 \cdot 54 \cdot 53}{6!}$

Simplify the numerator.

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Multiply $58$ by $57$ .

$\frac{3306 \cdot 56 \cdot 55 \cdot 54 \cdot 53}{6!}$

Multiply $3306$ by $56$ .

$\frac{185136 \cdot 55 \cdot 54 \cdot 53}{6!}$

Multiply $185136$ by $55$ .

$\frac{10182480 \cdot 54 \cdot 53}{6!}$

Multiply $10182480$ by $54$ .

$\frac{549853920 \cdot 53}{6!}$

Multiply $549853920$ by $53$ .

$\frac{29142257760}{6!}$

Simplify the denominator.

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Expand $6!$ to $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{29142257760}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Simplify.

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Multiply $6$ by $5$ .

$\frac{29142257760}{30 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Multiply $30$ by $4$ .

$\frac{29142257760}{120 \cdot 3 \cdot 2 \cdot 1}$

Multiply $120$ by $3$ .

$\frac{29142257760}{360 \cdot 2 \cdot 1}$

Multiply $360$ by $2$ .

$\frac{29142257760}{720 \cdot 1}$

Multiply $720$ by $1$ .

$\frac{29142257760}{720}$

Divide $29142257760$ by $720$ .

$40475358$

Find the Number of Possibilities 58 choose 6

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