# solution combinations

• December 22nd 2008, 01:41 PM
faruk_fin
solution combinations
I will have 7 numbers from 1 to 39. They can be any 7 numbers of 1 to 39. So how many parts i have to divide of those numbers. Example it can be 1,6,9,23,33,35,37 or other differents number. So can i have a solution of that?(Surprised)
• December 22nd 2008, 01:46 PM
Plato
Are you asking: "How subsets of seven numbers are there using the integers 1 to 39?"
• December 22nd 2008, 01:57 PM
Soroban
Hello, faruk_fin!

Quote:

I will have 7 numbers from 1 to 39. They can be any 7 numbers of 1 to 39.
So how many parts i have to divide of those numbers.
Example: it can be 1,6,9,23,33,35,37 or other differents number.
So can i have a solution of that?

I will assume the question is: In how may ways can we take 7 of 39 objects?

The answer is: . $_{39}C_7 \;=\;{39\choose7} \;=\;\frac{39!}{7!\,32!} \;=\;15,\!380,\!937$ ways.

• December 23rd 2008, 12:22 PM
faruk_fin
Thanks a lot.
But i want to know how many times i have to write those numbers 1 t0 39 n each time their will be 7 numbers. So if someone give me any 7 numbers of 1 to 39 at least their will be similarity once. Plz help me. Thanks again.(Worried)

Thanks a lot.
But i want to know how many times i have to write those numbers 1 t0 39 n each time their will be 7 numbers. So if someone give me any 7 numbers of 1 to 39 at least their will be similarity once. And how have to write all those numbers different time? Plz help me. Thanks again.(Worried)

Quote:

Originally Posted by Plato
Are you asking: "How subsets of seven numbers are there using the integers 1 to 39?"

It not that kind. I want know how many times i have to write those numbers n how many parts they will be. Each time ther will be 7 numbers they must to be 1 to 39. So any 7 numbers i get there will be similarity. Plz help.
• December 23rd 2008, 05:05 PM
Plato
Quote:

Originally Posted by faruk_fin
Quote:

Originally Posted by Plato
Are you asking: "How subsets of seven numbers are there using the integers 1 to 39?"

It not that kind. I want know how many times i have to write those numbers n how many parts they will be. Each time ther will be 7 numbers they must to be 1 to 39. So any 7 numbers i get there will be similarity. Plz help.

As much as you seem to dislike it, Soroban’s answer it the number that you for which you are asking.

If you disagree with me then you must make your question more mathematical meaningful?
• December 24th 2008, 12:46 PM
Soroban
Hello again, faruk_fin!

I'll take a guess at what you are asking . . .

We have a list of the 15,380,937 sets of seven numbers from the set 1-to-39.

. . $\begin{array}{c} \{1,2,3,4,5,6,7\} \\ \{1,2,3,4,5,6,8\} \\ \{1,2,3,4,5,6,9\} \\ \vdots \\ \{33,34,35,36,37,38,39\} \end{array}$

How many times does a particular number (say, 23) appear on the list?

I would conjecture that any number appears $\tfrac{1}{39}$ of the time.

Therefore, "23" appears $\frac{15,380,937}{39} \:=\:394,383$ times.