Question

What's the probability of drawing 7 preselected balls from a bowl of 35?

Answer 1

`1/(6,724,520)`

Explanation:

Let's imagine for a moment that the seven randomly chosen balls are 1, 2, 3, 4, 5, 6, 7. That is a unique combination and so there is only one way to achieve it.

The probability therefore will be:

`1/"number of possible combinations"`

So how many combinations are possible choosing 7 balls from a population of 35? The general formula is:

`C_(n,k)=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`

`C_(35,7)=(35!)/((7!)(35-7)!)=(35!)/(7!28!)=>`

`=> (35xx34xx33xx32xx31xx30xx29xx28!)/(7xx6xx5xx4xx3xx2xx28!)=>`

`=> 6,724,520`

And so the probability is:

`1/(6,724,520)`