What is (365!)/((365-5)!*365^5) ?

The solution to (365!)/((365-5)!*365^5) is (17267274024)/(365^4)

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simplify (365!)/((365-5)!*365^5)

simplify

\frac{365 !}{( 365 - 5 ) ! \cdot 36 5 ^{5}}

\frac{17267274024}{36 5 ^{4}}

Decimal

0.97286 \dots

Solution steps

\frac{365 !}{( 365 - 5 ) ! \cdot 36 5 ^{5}}

Subtract the numbers:

365 - 5 = 360

= \frac{365 !}{360 ! \cdot 36 5 ^{5}}

Cancel the factorials:

\frac{n !}{( n - m ) !} = n \cdot (n - 1) \dots (n - m + 1), n > m

\frac{365 !}{360 !} = 365 \cdot 364 \cdot 363 \cdot 362 \cdot 361

= \frac{365 \cdot 364 \cdot 363 \cdot 362 \cdot 361}{36 5 ^{5}}

Cancel

\frac{365 \cdot 364 \cdot 363 \cdot 362 \cdot 361}{36 5 ^{5}} : \frac{364 \cdot 363 \cdot 362 \cdot 361}{36 5 ^{4}}

= \frac{364 \cdot 363 \cdot 362 \cdot 361}{36 5 ^{4}}

Multiply the numbers:

364 \cdot 363 \cdot 362 \cdot 361 = 17267274024

= \frac{17267274024}{36 5 ^{4}}

\frac{3}{4} x - 5 + 1 \leq 16

(x + 3)^{2} = 3

\frac{9}{8} \cdot \frac{2}{3}

- \frac{1}{4} + \frac{1}{8}

\frac{1}{2} c + 3 < \frac{3}{4}

What is (365!)/((365-5)!*365^5) ?
The solution to (365!)/((365-5)!*365^5) is (17267274024)/(365^4)