there are 10 students in Mr. Alvarez's art class. Throughout the year, each student must pair up with every other student to complete a project. How many projects will be completed?
45?
combinations of ten taken two at a time:
10!/[(2!)(8!)] = 10*9/2 = 5*9 = 45
Grade 7 ????
I am trying to think how I would have done this in grade 7. I assume you have not had permutations, combinations and factorials.
make a table of combinations
first person shakes hands with 9 --> 9 projects
second with 8 --> 8 more
third with 7 --> 7 more
etc
9+8+7+6+5+4+3+2+1 = 45
4565
To find the number of projects that will be completed, we need to determine how many pairs can be formed among the 10 students.
To do this, we can use the formula for combinations, which is nCr = n! / (r! * (n-r)!), where n represents the total number of items and r represents the number of items selected.
In this case, we have 10 students and we need to select 2 students to form a pair. Thus, we can calculate the number of pairs using the formula:
10C2 = 10! / (2! * (10-2)!)
= 10! / (2! * 8!)
= (10 * 9 * 8!) / (2! * 8!)
= (10 * 9) / 2!
= 90 / 2
= 45
Therefore, there will be a total of 45 projects completed in Mr. Alvarez's art class.