How do you simplify the factorial expression $\frac{4!}{6!}$ $(4!)/(6!)$ ?

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Answer 1 · 2017-03-08T09:28:58

$\frac{1}{6 \times 5} = \frac{1}{30}$ $1/(6xx5)=1/30$

We can expand factorials into their constituent multiplication series:

$\frac{4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1}$ $(4xx3xx2xx1)/(6xx5xx4xx3xx2xx1)$

We can then cancel out the $4, 3, 2, and 1$ $4, 3, 2, and 1$ in both denominator and numerator and we're left with

$\frac{1}{6 \times 5} = \frac{1}{30}$ $1/(6xx5)=1/30$

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We could also express our initial problem as:

$\frac{4!}{6 \times 5 \times 4!}$ $(4!)/(6xx5xx4!)$ , cancel out the $4!$ $4!$ terms, and be left with $\frac{1}{30}$ $1/30$

How do you simplify the factorial expression 4!6!(4!)/(6!)?