Thread: How many combinations contain specific numbers?

Given are all possible combinations of 5 numbers from 1-35, all contained in combinations of 6 numbers (from 1-35). How many of the six number combinations contain 5 specific numbers?

Originally Posted by askjohn

Given are all possible combinations of 5 numbers from 1-35, all contained in combinations of 6 numbers (from 1-35). How many of the six number combinations contain 5 specific numbers?

Is it possible to give a clearer statement of this question?
As it reads now, you are asking “how many combinations of six contain a particular combination of given numbers?” The answer to that is 30.
But I cannot imagine that is what the question means. Is it?

Well, I'm a bit confused! That's what I thought at first too.

Since we are dealing with six number combinations, each one of which contains 6 possible combinations of five numbers, the total number of combinations of six containing all the combinations of five would be 324632 (35c5) / 6 = 54105 combinations of six; However, 35c6 would be 1623160.

So, if 30 were the answer to the first option, what would happen if we had all the combinations of 6 instead? Would it just be the same?

I just do not know what the OP means.
Is that an exact wording or is it a translation?

It's a translation.

Let me paraphrase.

We have all the possible combinations of five numbers from 1 to 35 (35c5) contained in combinations of six numbers.
for example: 1 2 3 4 5 6 (contains {1,2,3,4,5} {1,2,3,4,6} {1,2,3,5,6} {1,2,4,5,6} {1,3,4,5,6} {2,3,4,5,6})

What I want to know is how many of these -six- number combinations contain -five- specific numbers. Logically its 30. I'm confused however with the fact that every >1< combination of 6 contains 6 combinations of five!!

There are six combinations of six objects taken five at a time.

Hello, askjohn!

The wording is confusing.
All that emphasis on subsets of 5 numbers . . .

Given are all possible 6-number subsets of numbers from 1-35,
how many of these subsets contain 5 specific numbers?

What do you mean by "logically it's 30"? .Is that the correct answer?


Here's my reasoning . . .

The is one way to get the five specific numbers.
The sixth number can be any of the remaining 30 numbers.

Therefore, the answer is 30.

You're right! It's so simple.. I just got confused by the subsets within the subsets! thanks!