36. Find the number of ways in which six people can ride a toboggan if one of a subset of three must drive. 37. (a) Find the number of ways in which five persons can sit in a row. (b) How many ways are there if two of the persons insist on sitting next to one another? (c) Solve part (a) assuming they sit around a circular table. (d) Solve part (b) assuming they sit around a circular table. 38. Find the number of ways in which five large books, four medium-size books, and three small books can be placed on a shelf so that all books of the same size are together. 39. (a) Find the number of permutations that can be formed from the letters of the word ELEVEN. (b) How many of them begin and end with E? (c) How many of them have the three Es together? (d) How many begin with E and end with N? 40. (a) In how many ways can three boys and two girls sit in a row?
Answer: The number of ways in which six people can ride a toboggan if one of a subset of three must drive is 360.
Step-by-step solution
Step 1: Identify the driver
First, we need to choose one person from the subset of three to be the driver. Since there are 3 people in this subset, there are 3 possible choices for the driver.
Step 2: Arrange the remaining people
After selecting the driver, there are 5 people remaining. These 5 people can be arranged in the remaining 5 positions on the toboggan in (5 factorial) ways.
Step 3: Calculate the total number of ways
To find the total number of ways, we multiply the number of choices for the driver by the number of ways to arrange the remaining people. This gives us , which simplifies to .
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