Question

Solve by simplifying the problem. There are 18 students in Mr. Alvarez’s art class. Throughout the year, every student must pair up with every other student to complete a project. How many projects will be finished?

Answer 1

The answer to this complicated problem would be B.) 153 projects

Answer 2

153

Explanation:

There are 18 students in a class.

They are required to pair up with every other student to complete a project throughout the year .

Now we are asked to find the no. of projects will be finished .

So, we will use combination

Formula :
`_nC_r =(n!)/(r!(n-r)!)`

No. of students (n)=18

No. of students in each pair (r)= 2

Substituting the values in formula :

`_1_8C_2 =(18!)/(2!(18-2)!)`

`_1_8C_2 =(18!)/(2!(16)!)`

`_1_8C_2 =(18*17*16!)/(2!(16)!)`

`_1_8C_2 =(18*17)/(2*1)`

`_1_8C_2 =(306)/(2)`

`_1_8C_2 =153`

Thus the no. of projects will be finished is 153