Can 1/4 of the total combinations match 6 numbers drawn from a set of 80?

[StevieTNZ]

Hi there,

As my Maths skills suck, I'm not entirely sure if I've worked out the following correctly:

Using the combinations calculator - http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html - the total amount of possible numbers drawn in a game (80), and how many sets of 6 I can create using those 80 numbers (without repetition or order being important) - ends up to be 300,500,200.

In anyone game, 20 numbers of the 80 are drawn, which is equivalent to 1/4. Does that mean that 1/4 of the number of combinations I have - 300,500,200 - will match 6 of those numbers (out of 20) drawn?

E.g. I have the numbers 3, 4, 6, 10, 15, 25, 30, 45, 51, 58, 62, 63, 65, 67, 72, 73, 76, 77, 78, 80 drawn out of the 80.
One possible combination (of 6 numbers) is 15, 30, 62, 63, 78, 80. Since all six numbers are drawn, this ticket matches.

Not sure if that's clear enough, but my guess is that I need to work out the amount of combinations where n = 20 and r = 6.

But if we have n = 80, and r = 1, and 20 numbers are drawn (number of combinations being 80), 1/4 of the combinations (20) match a number drawn from a total of 80.

 

[Office_Shredder]

You can count how many combinations there are out of the 20 you have drawn by just seeing how many ways out of 20 numbers you can pick six of them

 

[StevieTNZ]

Thanks for that. I thought that was the way to go about it.