Six people are going to be seated in a row of 8 chairs. How many different ways may they be seated?
To find the number of different ways the six people can be seated in a row of eight chairs, we can use the concept of permutations.
A permutation is an arrangement of objects in a specific order. In this case, we want to arrange the six people in a row of eight chairs, without any restrictions.
Since there are no restrictions on the seating arrangement, we can use the formula for permutations of n objects taken r at a time, which is given by:
P(n, r) = n! / (n - r)!
In this case, there are 6 people to be seated in 8 chairs, so we are finding the permutation of 6 objects taken 6 at a time.
Using the formula, we have:
P(6, 6) = 6! / (6 - 6)!
= 6! / 0!
= 6! / 1
= 6!
Now, let's calculate 6! (factorial of 6):
6! = 6 * 5 * 4 * 3 * 2 * 1
= 720
Therefore, there are 720 different ways the six people can be seated in a row of eight chairs.