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Calculating combinations

Calculating values of N choose M, including with multiplication and division

The skill being taught is how to calculate the values of combinations, specifically "N choose M". This process involves using factorials to determine the number of combinations by dividing the factorial of N by the product of the factorial of M and the factorial of (N-M).

Learn calculating combinations

Teaching Transcript

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What is the value of this probability expression?

First let's change it from binomial form so it might be a little easier to talk about.

Now we can start tackling one term at a time. Let's start on the top with 4 choose 2. That's 4 factorial, over 2 factorial, multiplied by, 4 minus 2 factorial

Calculating that term, its value is 6, so we can plug that in.

Now let's move to the bottom and tackle 2 choose 2. That's 2 factorial, over 2 factorial, multiplied by, 2 minus 2 factorial

Since both zero and one, factorial, are just 1, our value is 1, so we can plug that in.

Now our final term is 3 choose 2. That's 3 factorial, over 2 factorial, multiplied by, 3 minus 2 factorial

Which has a value of 3

With all terms calculated, we can see that our expression's value is 2

Skill Practice

Calculating values of N choose M, including with multiplication and division

Test your understanding of calculating combinations by practicing it! Work through the below exercises to use it in practice.