A bag contains 5 identical red counters, 3 identical blue counters, and 1 green counter. If 3 counters are selected from the bag, how many different possible sets of counters could be selected?

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Official Explanation

Official

3 counters can be distributed among 3 color buckets as follows:

\frac{5!}{3!2!} = 10

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However, this allows for 2 and 3 counters to be allocated to green, where only 1 is available. Subtract these instances:

- 2 counters: remaining counter can be distributed 2 ways.…

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.