**Solutions**

*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.*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 toso this solution is checking.

*Read and understand the question*. This question is looking for the total number of combinations of 6 students taken 4 at a time.

*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.

*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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