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

Answer:

153

Step-by-step 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 : $_nC_r =\frac{n!}{r!(n-r)!}$

No. of students (n)=18

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

Substituting the values in formula :

$_1_8C_2 =\frac{18!}{2!(18-2)!}$

$_1_8C_2 =\frac{18!}{2!(16)!}$

$_1_8C_2 =\frac{18*17*16!}{2!(16)!}$

$_1_8C_2 =\frac{18*17}{2*1}$

$_1_8C_2 =\frac{306}{2}$

$_1_8C_2 =153$

Thus the no. of projects will be finished is 153

Answer 2

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