how many different seating arrangements are possible for 6 people in 4 chairs?
I think 15 correct me pls or help me
there are 6 people
you need to choose 4 of them to be seated (in chairs)
There are 6 choices for the 1st chair
for the 2nd chair, there are now 5 people left to choose from
so, there are 6*5 ways to put people in the 1st 2 chairs.
Then, there are 4 ways to pick the 3rd person
and only 3 ways to pick the 4th person
6*5*4*3 = 360
6P4 = 6! / (6-4)! = 360
There are 6C2 = 15 ways to choose the 4 people, if you don't care where they sit. But there are 4! ways to rearrange the 4 people once they have been chosen. 15*24 = 360
But these 6 people not 4
And there’s 4 chairs
To determine the number of different seating arrangements for 6 people in 4 chairs, you can use the concept of permutations.
In this case, you need to find the number of permutations of 6 people taken 4 at a time because you have 4 chairs available.
The formula to calculate permutations is:
nPr = n! / (n - r)!
Where "n" is the total number of items and "r" is the number of items taken at a time.
Applying the formula to your problem:
6P4 = 6! / (6-4)!
Calculating the factorial values:
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
(6-4)! = 2! = 2 x 1 = 2
Substituting the values:
6P4 = 720 / 2
= 360
So, there are 360 different seating arrangements possible for 6 people in 4 chairs.
Therefore, your initial guess of 15 is incorrect, and the correct answer is 360.