# Let's play a game of probability

**Discrete Mathematics**Level 3

Ahmed played a game at the fair. He had to pick 2 balls from a basket of 50 whilst blindfolded.

There were a range of different \(\color{blue}{c}\color{red}{o}\color{green}{l}\color{pink}{o}\color{orange}{u}r\color{purple}{e}\color{indigo}{d}\) balls in the bag. He tooked 2 out and handed them to a lady running the game. Both balls were **black**. She looked at the 2 balls and said:

\[\text{“The probability of you doing that is }\large\frac{4}{175}\text{"}\]

Given that there were at least three different types of colors of balls in the basket, find the maximum number of \(\color{red}{red}\) balls in the bag.

**Clarification:** There is at least one red ball in the basket.