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Worksheet on Combinations and Permutations

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Permutations and combinations are easy to get confused. They are both ways to count r things taken from a set of n distinct objects, but the way that we count is different.

The key thing to remember is that permutations deal with situations when the order that we choose the objects or arrange them is important. In combinations we are not concerned with what order we selected our objects. We only need this concept, and the formulas for combinations and permutations to solve problems dealing with this topic.

Here are some practice problems help you straighten out the ideas of permutations and combinations. Solutions to these problems are here.

  1. Calculate P( 5, 2 ).
  2. Calculate C( 5, 2 ).
  3. Calculate P( 6, 6 ).
  4. Calculate C( 6, 6 ).
  5. Calculate P( 100, 97 ).
  6. Calculate C( 100, 97 ).
  7. It’s election time at a high school that has a total of 50 students in the junior class. How many ways can a class president, class vice president, class treasurer,and class secretary be chosen if each student may only hold one office?
  8. The same class of 50 students wants to form a prom committee. How many ways can a four person prom committee be selected from the junior class?
  9. If we want to form a group of five students and we have 20 to choose from, how many ways is this possible?
  10. How many ways can we arrange four letters from the word “computer” if repetitions are not allowed, and different orders of the same letters count as different arrangements?
  11. How many ways can we arrange four letters from the word “computer” if repetitions are not allowed, and different orders of the same letters count as the same arrangement?
  12. How many different four digit numbers are possible if we can choose any digits from 0 to 9 and all of the digits must be different?
  13. If we are given a box containing seven books, how many ways can we arrange three of them on a shelf?
  14. If we are given a box containing seven books, how many ways can we choose collections of three of them from the box?
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