5th Combinatorial question

1. Jul 18, 2007

pivoxa15

1. The problem statement, all variables and given/known data
To win Division 1 in the game of Tattslotto, the player must have the same 6 numbers (in any order) as those that are randomly drawn from the numbers 1 to 45. A Division 2 prize requires that the player’s ticket must have 5 of the 6 winning numbers and a Division 3 prize requires that the player has 4 of the 6 numbers drawn. Calculate the probability that the player’s 6 numbers will contain at least a Division 3 prize.

2. Relevant equations
Pr(event) = Favourable possibilities/total possibilities

C means ‘choose’ i.e. nCr=n!/(r!(n-r)!)

3. The attempt at a solution
Assume player has chosen their 6 numbers and the officials have drawn the 6 numbers.

Favourable possibilities = {6C6=1, 6C5=6, 6C4=15}
Total possibilities = 45C6

Pr(event) = (1+6+15)/45C6 = 22/8145060

2. Jul 18, 2007

neurocomp2003

have you learned the inclusion /exclusion principle...if not i suggest looking it up.

If you cant find it then think about what are the relations between
6C6 6C5 6C4

also your summation is wrong...reread the quesiton particularly the last 2 statements.

3. Jul 18, 2007

Dick

Funny. I get 1135/814506. Your stated answer is not in lowest terms, so I suspect a typo. You are only accounting for the ways of choosing winning numbers, you have to choose the correct number of losing numbers in each case as well.

4. Jul 18, 2007

pivoxa15

I am a bit lost here. I understand the inclusion/exclusion principle but don't see how it's applied here.

5. Jul 18, 2007

Dick

I don't either, but there are many more ways of picking four winning numbers than 6C4. You have two more numbers to choose.

Last edited: Jul 18, 2007
6. Jul 18, 2007