Determining the number of seating arrangements with 10 people in 7 chairs requires use of?
Permutation formula.
To determine the number of seating arrangements with 10 people in 7 chairs, you need to use the concept of permutations.
The formula to calculate permutations is given by:
P(n, r) = n! / (n - r)!
where n is the total number of items to choose from, and r is the number of items to be arranged.
In this case, the number of people (n) is 10, and the number of chairs (r) is 7.
So, the formula becomes:
P(10, 7) = 10! / (10 - 7)!
Simplifying further:
P(10, 7) = 10! / 3!
Now, let's calculate:
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800
3! = 3 x 2 x 1 = 6
Substituting the values:
P(10, 7) = 3,628,800 / 6 = 604,800
Therefore, the number of seating arrangements with 10 people in 7 chairs is 604,800.