SAT Math Multiple Choice Practice Question 366: Answer and Explanation

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Question: 366

14. In how many different ways can five students of different heights be arranged in a line if the tallest student cannot be on either end?

A. 24
B. 25
C. 72
D. 96
E. 120

Correct Answer: C


C To arrange these students, five choices must be made. First select the students for each end. Since one of the five (the tallest) cannot go on either end, you have four students to choose from for one end, and then, once that choice has been made, three students to choose from for the other end:

Now fill the remaining spots. There are three students left to choose from for the second spot:

Then, once that selection has been made, there are two for the next spot, then one for the remaining spot:

To find the total number of possible arrangements, simply multiply:.

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