# Counting Methods ???

• Nov 3rd 2008, 12:00 AM
Counting Methods ???
In a lotto, a player picks a selection of 6 numbers from the numbers 1 to 45. To determine the winners 8 numbers are chosen at random - the first 6 are designated as the winning numbers, and the other 2 as supplementary numbers.
Division 1: 6 winning numbers
Division 2: 5 winning numbers and 1 supplementary
Division 3: 5 winning '
Div 4: 4 winning '
Div 5: 3 winning ' and 1 supplementary
Find the number of combinations which satisfy each of the divisions, and hence the probabilities of winning each of the five divisions.

I don't get a word of it....
• Nov 10th 2008, 05:55 PM
Rapha
Quote:

In a lotto, a player picks a selection of 6 numbers from the numbers 1 to 45. To determine the winners 8 numbers are chosen at random - the first 6 are designated as the winning numbers, and the other 2 as supplementary numbers.
Division 1: 6 winning numbers
Division 2: 5 winning numbers and 1 supplementary
Division 3: 5 winning '
Div 4: 4 winning '
Div 5: 3 winning ' and 1 supplementary
Find the number of combinations which satisfy each of the divisions, and hence the probabilities of winning each of the five divisions.

I don't get a word of it....

Well 6 winning numbers, how many combinations exist?

\$\displaystyle {45 \choose 6} = 8,145,060\$

thus the probability p(6 winning numbers) = 1 / 8,145,060

and so on...