5th - 8th grade

Bill has 7 students in his basketball team. Only 5 can play at once. How many different groups of 5 students can have on the court at a time?

Hint: it's easier to think of the reverse of this questions - how many different groups of 2 students can sit on the bench.

5th - 7th grade

Mathnasium has a "perfect page day" whenever a student correctly guesses the roll of a 6 sided die. There is one chance per day. If Mathnasium is open 5 days per week, on average how many perfect page days will there be per year?

7th - 11th grade

In Deal or no Deal 1 case is worth $1 Million. The other cases are not. The player selects a case, then begins to open the other cases. After 18 cases have been opened and found to not have the $1 Million, there are two cases left. The player then has a chance to switch cases. Should the player switch cases?


Hint: What is the probability the $1 million is in the original case, and what is the probability that it is in the other case? They're not the same!

11th grade

6 students are waiting in line for lunch. How many different ways can those 6 students order themselves in line?

5th-11th grade

At the G20 summit, 20 top world leaders get together. If every leader shakes every other leader's hand once, how many total hand shakes will occur?