Six people are going to be seted in a row of 8 chairs. How many different ways may they be seated?
To determine the number of different ways the 6 people can be seated in a row of 8 chairs, you need to calculate the number of permutations.
The number of permutations is given by the formula nPr = n! / (n - r)!, where n is the total number of items you have and r is the number of positions you need to fill.
In this case, you have 6 people to seat and 8 chairs to choose from. Therefore, n = 8 and r = 6.
Calculating the permutation value:
6P6 = 6! / (6 - 6)!
= 6! / 0!
= 6! / 1
= 6!
Using the factorial definition, 6! = 6 × 5 × 4 × 3 × 2 × 1, the calculation becomes:
6! = 6 × 5 × 4 × 3 × 2 × 1
= 720
Thus, there are 720 different ways the 6 people can be seated in a row of 8 chairs.