Question

A high school auditorium seats 110 people. The school play has 106 people in attendance leaving 4 seats empty.because the order in whichThere are ( 5,773,185, 6, 913,340, 2,141, 851,635, and 138,556,440)the seats are chosen (is not, is)ways that 4 seats can be left empty in the auditorium. This is a ( permutation, combination)important.A high school auditorium seats 110 people. The school play has 106 people in attendance leaving 4 seats empty.

Answer 1

The answers are :

5,773,185

is not

combination

EXPLANATION :

There are 110 seats.

and there are 110 ways to choose the first empty seat

Now, there are 109 seats left.

and there are 109 ways to choose the second empty seat

Now, there are 108 seats left

and there are 108 ways to choose the third empty seat

Now, there are 107 seats left

and there are 107 ways to choose the fourth empty seat

The total number of ways is the product of the result above :

110 x 109 x 108 x 107 = 138,556,440

We will divide this to 4! or 4 x 3 x 2 x 1 = 24

Since the order is not important.

That will be :

`138,556,440/24=5,773,185`

Since the order is not important, this is a combination problem.