In how many ways can a 6 people sit in a toboggan (sled) if only 2 can drive?
Well, if only 2 people can drive the toboggan, then that means the other 4 people can just sit back and enjoy the ride! So, we only need to worry about the seating arrangement for the 2 drivers.
Assuming the toboggan does not have designated seats, we can calculate the number of ways the 2 drivers can sit using the combination formula. We choose 2 drivers out of the 6 people, so the number of ways they can sit is given by:
C(6, 2) = 6! / (2! * (6-2)!) = 15.
So, in this case, there are 15 different ways the 6 people can sit in the toboggan, considering only 2 can drive. Happy sledding!
To determine the number of ways 6 people can sit in a toboggan, taking into account that only 2 can drive, we can follow these steps:
Step 1: Determine the number of ways to select the 2 people who can drive. This can be done using the combination formula (nCr), where n is the total number of people (6) and r is the number of people who can drive (2).
nCr = n! / (r!(n-r)!)
= 6! / (2!(6-2)!)
= 6! / (2! 4!)
= (6 * 5 * 4!) / (2! 4!)
= (6 * 5) / 2!
= 30 / 2
= 15
Step 2: Once the drivers are selected, the remaining 4 people can sit in any order. This can be calculated using the factorial of the number of remaining people (4!).
4! = 4 * 3 * 2 * 1
= 24
Step 3: Finally, multiply the results from Step 1 and Step 2 to get the total number of ways.
Total number of ways = Number of ways to select drivers * Number of ways for remaining people
= 15 * 24
= 360
So, there are 360 ways in which the 6 people can sit in the toboggan, considering that only 2 can drive.
To determine the number of ways the 6 people can sit in a toboggan, while also accounting for the condition that only 2 can drive, we can use the concept of permutations.
Let's break down the steps:
Step 1: Selecting the 2 drivers
Since only 2 people can drive, we need to select 2 out of the 6 people to be the drivers. This can be done using combinations. The number of ways to select 2 drivers out of 6 is denoted by "C(6, 2)" or "6 choose 2", which can be calculated as:
C(6, 2) = 6! / (2!(6-2)!)
= 6! / (2!4!)
Step 2: Arranging the remaining 4 passengers
Once we have selected the 2 drivers, we have 4 remaining people to arrange on the toboggan. Since order matters, we can use permutations for this step. The number of ways to arrange 4 people is denoted by "P(4, 4)" or "4 permutation 4", which can be calculated as:
P(4, 4) = 4!
Step 3: Combining the results
To find the total number of ways the 6 people can sit in the toboggan with only 2 drivers, we need to multiply the results from Step 1 and Step 2 together:
Total number of ways = C(6, 2) * P(4, 4)
= (6! / (2!4!)) * 4!
Now we can calculate the result:
Total number of ways = (6 * 5 / (2 * 1)) * (4 * 3 * 2 * 1)
= 15 * 24
= 360
Therefore, there are 360 ways for 6 people to sit in a toboggan, satisfying the condition that only 2 people can drive.
I used to have one of those long toboggans.
Everybody just piled on, no social distancing.
2 drivers, then ....
number of ways to sit:
2 * 5!
= ....