Question

A raffle is held at the local community center and 200 tickets are sold. Three names will be drawn for the winning tickets. If the order doesn't matter, how many winning combinations of people are possible.

Answer 1

1,313,400 winning combinations of people are possible

Explanation:

Total number of tickets sold = 200

This means there are total 200 possible options for the winning tickets and only 3 winners will be selected. So we have to select 3 winners out of 200. It is stated that the order of selection doesn't matter, this means this is a problem of combinations.

Winning combinations of 3 people out of 200 means, we have to find the number of combinations of 200 people taken 3 at a time which can be represented as 200C3.

The formula for combinations is:

`^(n)C_(r)=(n!)/(r!(n-r)!)`

So, for the given case it would be:

`^(200)C_(3)=(200!)/(3! * (200-3)!)\\\\ =(200!)/(3! * 197!)\\\\ = 1313400`

This means, 1,313,400 winning combinations of people are possible.