Exploring the Endless Combinations: How Many Ways Can Julia Make a Platter with 4 Types of Cheese and 4 Types of Crackers?

When it comes to creating a cheese and cracker platter, the possibilities can seem endless. With a variety of cheeses and crackers to choose from, the combinations can be overwhelming. But have you ever wondered exactly how many combinations there could be? Let’s take a closer look at this question using a scenario where Julia has seven different types of cheese and six different types of crackers, and she wants to make a platter with four types of each.

Understanding the Basics of Combinations

Before we dive into the calculations, it’s important to understand the basics of combinations. In mathematics, a combination is a selection of items without considering the order. This means that if Julia chooses cheddar, brie, gouda, and camembert cheeses, it would be considered the same combination as brie, gouda, camembert, and cheddar.

Calculating the Number of Cheese Combinations

To calculate the number of ways Julia can choose four cheeses out of seven, we use the combination formula: C(n, r) = n! / r!(n-r)!, where n is the total number of items, r is the number of items to choose, and ! denotes factorial. Plugging in our values, we get C(7, 4) = 7! / 4!(7-4)! = 35. So, there are 35 different ways Julia can choose four cheeses.

Calculating the Number of Cracker Combinations

Similarly, to calculate the number of ways Julia can choose four crackers out of six, we use the same combination formula. Plugging in our values, we get C(6, 4) = 6! / 4!(6-4)! = 15. So, there are 15 different ways Julia can choose four crackers.

Calculating the Total Number of Platter Combinations

To find the total number of ways Julia can make the platter, we multiply the number of cheese combinations by the number of cracker combinations. So, 35 cheese combinations times 15 cracker combinations equals 525. Therefore, there are 525 different ways Julia can make a platter with four types of cheese and four types of crackers.

Conclusion

So, the next time you’re faced with a variety of cheeses and crackers, remember that the possibilities are vast. Whether you’re a fan of sharp cheddar or creamy brie, salty crackers or sweet, there’s a combination out there for everyone. And who knows? You might just discover your new favorite pairing.