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Lionel poses the question, "How do I decide if I should use the formula for the number of permutations or the number of combination? For example, I had the following question in the homework: On a test, a student is to answer 10 out of 13 questions. How many ways can this be done?
Lionel, that is a very good question. Simply stated, a permutation is an order, an arrangement. A combination is a set of objects, a collection of objects, without regard to order. "Order" becomes the operative word.
Thus, the number of permutations of 13 items taken 10 at a time means the number of orders of 10 items taken from 13 items. And the number of combinations of 13 items taken 10 at a time means the number of collections of 13 items we can form from 13 items.
In your example, the question is, does it matter which order the 10 questions are selected? If order does, we use the number of permutation. If order does not matter, we use the number of combinations. The example by itself is unclear if we are to determine the number of orders or the number of sets of 10 questions we are to determine.
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