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Total outcome counting with cards

Counting ways to pick N cards from M total cards

This math skill teaches how to calculate the number of ways to choose N cards from a total of M cards using combinations (binomial coefficients). It explains the formula for combinations as M factorial divided by N factorial times (M-N) factorial.

Learn total outcome counting with cards

Teaching Transcript

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How many different ways can we draw 2 cards from this hand of 8 cards?

To phrase this in a way that will help find the right formula, we are are looking to pick 2 from 8 in any order.

So that's 8 choose 2, or, in binomial notation, 8 over 2 in brackets

The factorial equation for 8 choose 2 is 8 factorial, divided by, 2 factorial times 8 - 2 factorial.

If we calculate that out, that's 28 unique ways to pick 2 letter tiles if order doesn't matter

Skill Practice

Counting ways to pick N cards from M total cards

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