# Thread: Chance of guessing 4 numbers from 7 - should be easy!?

1. ## Chance of guessing 4 numbers from 7 - should be easy!?

I have what appears (to my non-mathematical brain) to be a relatively simple probability problem, but I don't know how to go about solving it. Perhaps someone here could help, and "explain their working" so that I can figure it out for myself in future.

Here's the problem:

• I choose 4 numbers from 1-49
• A random number generator selects 7 numbers from 1-49, with each number only appearing once
• What is the probability that my 4 chosen numbers all appear within the selection of 7?
• The sequence in which the numbers appear is not important.

2. ## Re: Chance of guessing 4 numbers from 7 - should be easy!?

4 numbers need to be "matched"; so:
4/49 * 3/48 * 2/47 * 1/46 = 1/211876 ;
same as 49C4.

3. ## Re: Chance of guessing 4 numbers from 7 - should be easy!?

Originally Posted by visualthinker
• I choose 4 numbers from 1-49
• A random number generator selects 7 numbers from 1-49, with each number only appearing once
• What is the probability that my 4 chosen numbers all appear within the selection of 7?
• The sequence in which the numbers appear is not important.
There are $_{49}\mathscr{C}_7=\dbinom{49}{7}=85,900,584$ ways for the random number generator to select 7 numbers from 1-49. Of those there are $_{45}\mathscr{C}_3=\dbinom{45}{3}=14,190$ which contain any four given (selected) numbers.