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 : [tex]_nC_r =\frac{n!}{r!(n-r)!}[/tex]
No. of students (n)=18
No. of students in each pair (r)= 2
Substituting the values in formula :
[tex]_1_8C_2 =\frac{18!}{2!(18-2)!}[/tex]
[tex]_1_8C_2 =\frac{18!}{2!(16)!}[/tex]
[tex]_1_8C_2 =\frac{18*17*16!}{2!(16)!}[/tex]
[tex]_1_8C_2 =\frac{18*17}{2*1}[/tex]
[tex]_1_8C_2 =\frac{306}{2}[/tex]
[tex]_1_8C_2 =153[/tex]
Thus the no. of projects will be finished is 153
