Six people are going to be seated in a row of 8 chairs. How many different ways may they be seated?
To determine the number of different ways six people can be seated in a row of eight chairs, we can use the concept of permutations.
In this scenario, we have six individuals and eight chairs, which means that six places need to be filled.
To calculate the number of ways those six individuals can be seated, we compute the permutation of six taken from eight, denoted as P(8,6) or 8P6.
The formula for a permutation of n objects taken r at a time is given by:
P(n,r) = n! / (n-r)!
Where "!" denotes the factorial function.
Thus, for this problem, we have:
P(8,6) = 8! / (8-6)!
= 8! / 2!
= 8 x 7 x 6 x 5 x 4 x 3
= 20160
Therefore, there are 20,160 different ways the six people can be seated in a row of eight chairs.
6P4
= 6!/(6-4)!
=6*5*4*3*2*1/2!
=6*5*4*3*2*1/2*1
=720/2
=360.
(/)-represents division.
(*)-represents multiplication.
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