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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?

User Gschambial
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2 Answers

5 votes
The answer to this complicated problem would be B.) 153 projects
User Zardon
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1 vote

Answer:

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

User Steve Oh
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