Find the number of ways in which six people can ride toboggan if one of three must drive
To determine the number of ways the six people can ride the toboggan with one of three driving, we need to consider the positions of the driver and the remaining five passengers.
Firstly, we can choose one person to be the driver in three ways. Once the driver is chosen, we are left with five remaining passengers.
Next, we need to arrange these five passengers in the remaining spots on the toboggan. The order in which they sit does matter, so we will use permutation formula.
There are 5 choices for the first remaining passenger, 4 choices for the second passenger, 3 choices for the third passenger, 2 choices for the fourth passenger, and only 1 choice for the final passenger.
Therefore, the total number of ways in which six people can ride the toboggan with one of three driving is:
3 * 5 * 4 * 3 * 2 * 1 = 3 * 5! = 3 * 120 = 360 ways.
To find the number of ways in which six people can ride a toboggan if one of them must drive, we use the concept of permutation.
First, we choose one person to be the driver. There are three options for this.
Next, we need to consider the remaining five people who will ride as passengers. We can arrange them in any order.
The number of ways to arrange five people is given by 5 factorial (5!), which is equal to 5 x 4 x 3 x 2 x 1 = 120.
Therefore, the total number of ways in which six people can ride a toboggan with one of them driving is:
3 (choices for the driver) multiplied by 120 (arrangements for the remaining passengers) = 360 ways.