# Odds of Winning a Raffle

There's a raffle:

• 754 total entries in the raffle
• 130 will get selected

What's the odds that I will get selected?

## 2nd Question:

Now, what if I have 4 of the 754 entries? What are my odds then?

Can you walk me through the math on this?

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Odds ... and my guess for the first part was 130/754. I have no clue how to solve the 2nd part. – Martin Sep 24 '13 at 15:43

## 2 Answers

Hint: if you have multiple tickets, calculate the chance that you do not win and subtract from $1$. What is the chance that your first ticket loses? Given that it does, what is the chance that the next one loses-how many numbers are left?

Added: to get the chance that you have two winners out of four, you have {6 \choose 2} ways to choose the winners, so the chance is ${6 \choose 2}\cdot \frac {130}{754}\cdot \frac {129}{753} \cdot \frac {624}{752} \cdot \frac {623}{751}$. The others are similar.

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Hints: How many different ways are there to choose $130$ of $754$ tickets?

If you have just one entry, then in how many ways can one of the chosen $130$ entries be yours and $9$ of them belong to other people?

If you have $4$ entries, then in how many ways can all $130$ chosen entries belong to someone else? How many ways, then, can at least one of your entries be chosen?

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