SOLUTION: Mr. Roland, an elementary school teacher, has 24 students. Every day he picks two students to be his "special helpers" for the day. How many pairs of students are there in the clas

Question 161300This question is from textbook
: Mr. Roland, an elementary school teacher, has 24 students. Every day he picks two students to be his "special helpers" for the day. How many pairs of students are there in the class? If the school year is 190 days long, will there be enough days for every pair of children to the be "special helpers"? (Notice that the problem asks about every pair of children, not every individual child.) Explain your reasoning. This question is from textbook

Found 2 solutions by stanbon, schrammbledeggs:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The number of pairs is 24*23 = 552
Cheers,
Stan H.
Answer by schrammbledeggs(41) (Show Source): You can put this solution on YOUR website!
So let's start with Student 1...he can be partners with every single person in the class...so that's 23 people who can be partners with student 1 and therefore 23 pairs right there.
Onto student 2...he can be partners with everyone in his class EXCEPT student 1 cause they've already been partners before...so he gets 22 more people...which equals 22 more pairs right there.
This sequence goes on and on until only 1 unique pair is left.
Therefore...mathematically represented...the problem is...
23+22+21+20+19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1...
Which = 276
Therefore, no, there are not enough school days for every pair of children to be "special helpers."
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