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Total outcome counting with letters

Counting ways to pick N tiles from M total tiles

This math skill teaches how to calculate the number of different ways to select a subset of tiles from a larger set using combinations. Specifically, it explains using binomial coefficients or "n choose k" notation, using factorials to determine the number of unique combinations possible when order does not matter.

Learn total outcome counting with letters

Teaching Transcript

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How many different ways can we draw 2 tiles from this set of 6 letter tiles?

To phrase this in a way that will help find the right formula, we are are looking to pick 2 from 6 in any order.

So that's 6 choose 2, or, in binomial notation, 6 over 2 in brackets

The factorial equation for 6 choose 2 is 6 factorial, divided by, 2 factorial times 6 - 2 factorial.

If we calculate that out, that's 15 unique ways to pick 2 letter tiles if order doesn't matter

Skill Practice

Counting ways to pick N tiles from M total tiles

Test your understanding of total outcome counting with letters by practicing it! Work through the below exercises to use it in practice.