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# Word Problems with the Counting Principle, Permutations and Combinations Practice Questions (page 3)

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#### Solutions

1. Read and understand the question. This question is looking for the total number of combinations of 2 books selected from a series of 4 books.
2. Make a plan. Because the order is not important, find the number of permutations of 4 books taken 2 at a time, and then divide by the number of permutations of 2 books taken 2 at a time.

Carry out the plan. The number of permutations of 4 students taken 2 at a time is equal to 4 × 3 and the total number of permutations of 2 books taken 2 at a time is equal to 2 × 1. Divide to find the total number of combinations of 4 books taken 2 at a time: different combinations.

Check your answer. To check this solution, reevaluate the number of combinations. The number of combinations is equal to, so this solution is checking.

3. Read and understand the question. This question is looking for the total number of combinations of 8 movies taken 4 at a time.

Make a plan. Because the order is not important, find the number of permutations of 8 movies taken 4 at a time, and then divide by the number of permutations of 4 movies taken 4 at a time.

Carry out the plan. The number of permutations of 8 movies taken 4 at a time is equal to 8 × 7 × 6 × 5 and the total number of permutations of 4 movies taken 4 at a time is equal to 4 × 3 × 2 × 1. Divide to find the total number of combinations of 8 movies taken 4 at a time:

different combinations.

Check your answer. To check this solution, reevaluate the number of combinations. The number of combinations is equal to

so this solution is checking.

4. Read and understand the question. This question is looking for the total number of combinations of 6 students taken 4 at a time.
5. Make a plan. Because the order is not important, find the number of permutations of 6 students taken 4 at a time, and then divide by the number of permutations of 4 students taken 4 at a time.

Carry out the plan. The number of permutations of 6 students taken 4 at a time is equal to 6 × 5 × 4 × 3 and the total number of permutations of 4 students taken 4 at a time is equal to 4 × 3 × 2 × 1. Divide to find the total number of combinations of 6 students taken 4 at a time:

different combinations.

Check your answer. To check this solution, reevaluate the number of combinations. The number of combinations is equal to

so this solution is checking.

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