How many combinations of 10 numbers are possible from 20 numbers?

Question

Need some help!!!!

In a lottery where you have 20 numbers.

how many 10 number combinations are possible from 20 numbers?

how many 9 number combinations are possible from 20 numbers?

how many 8 number combinations are possible from 20 numbers?

how many 7 number combinations are possible from 20 numbers?

how many 6 number combinations are possible from 20 numbers?

Order of the numbers doesn't matter.

Is there a formula that can be used allowing a choice of Total numbers and allowing a choice of various combinations?

Thanks Michael W

Answer 1

There is a function in the Excel spreadsheet which most people have on their computer. It is combin(m,n) which is short for combinatorial. For instance combin(20,10)=184,756 which is the answer to your first question.

  The other respondents answered this question correctly, but the spreadsheet just makes the calculation easier.

  The function is not included in the Microsoft Works spreadsheet.

Answer 2

The number of combinations of 10 from 20 is 184,756.

The formula is n!/(k!*(n-k)!)

http://mathforum.org/dr.math/faq/faq.com...

Answer 3

My guess based on faded memories of statistics :)  Hope someone else can verify or provide the correct answer...

20!-10!    that is ( 1X2X3X.....19X20 ) - (1X2X3...X9X10)

and for the others... 20!-9!, 20!-! etx...

The ! means factorial...

yup - sagmo below is correct...