# Simple Maths Riddle 6

A sixth riddle!

There's a function just

(reserved)

for me

though you need three

of me to complete it.

Don't simplify

(me)

when the top's much larger;

I'll explode

before you know it.

What am I?

I think it may be (only may be , not sure!!!)

Combinatorics (combinations)

There's a function just (reserved) for me

though you need three of me to complete it.

Expression : $$^nC_r$$ - three symbols required to complete the expression, also $$^nC_r = \frac{n!}{r!(n-r)!}$$ - three 'factorial' terms

Don' t simplify when the top's much larger

Evaluating $$^nC_r$$ becomes tedious, if $$n$$ is large, (provided $$r$$ is not very large or small ) .  For e.g, $$^{520}C_{14} = 1016179801403563036214357760$$

I'll explode before you know it

May be the same as above or combinatorial explosion https://en.wikipedia.org/wiki/Combinatorial_explosion

• Thank you! Is it really correct? – Ak19 May 20 at 6:35
• Yep! Note that the function was originally a reference to the hypergeometric distribution with parameters given by $\sf{Hy(x\mid N,d,n)}$ and density function $$p(x)=\frac{\binom dx \binom{N-d}{n-x}}{\binom Nn}$$ and as you can see, it is made up of three combinations. Great job! – TheSimpliFire May 20 at 6:38
• Thanks a lot!!! – Ak19 May 20 at 6:38

First Attempt (possibility to be correct: 20%)

cone?

There's a function just

(reserved)

for me


Volume of a cone : $$pi*r^2*h/3$$

though you need three

of me to complete it.


denominator = $$3$$, complete: without it?

Don't simplify

(me)

when the top's much larger;

I'll explode


pi is just sooooo long... when simplified...

before you know it.