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Math Problem - Can anyone solve this probability problem?

Leaving Cert Student

In the National Lottery, forty five balls numbered 1 to 45 are placed in a drum.
Six balls are taken at random from the drum as the winning combination.
If you select six numbers from 1 to 45, what is the probability that, at most,
only one of them matches with the winning combination?
Give your answer in decimal form, correct to two decimal places.

Answer: 0.82

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Leaving Cert Student

anyone show how to get this answer please?

TheChizler

Can you show what you've got so far?

Leaving Cert Student

TheChizler wrote: »

Can you show what you've got so far?

I don't know how to do it to be honest. All I have done is 45C6 and it gives approx 8 million different ways of choosing 6 from 45 so I assume thats the total. What to do after that is puzzling me...?

Derpington95

We havent done that chapter yet but ill try help.
Doing 45C6 means there are 8145060 possible combinations disregarding order. Say the winning number consisted of a,b,c,d,e,f
These 6 numbers can be arranged in 6! (720) winning ways.
So you must find out the odds of those 6 numbers coming up in any order multiplied by the odds of picking one number of the 6 Probably worng but at least i tried :P? Thats what i'm guessing we havent done that yet since im only a smelly 5th year

Leaving Cert Student

Ok I got help off my teacher for this one thank you very much for your reply derpington a true gentleman

.

The way you'd do this is get the total as you said 45 C6.
Then get the total ways of getting zero: 39c6
and the total ways of getting 1: 39C5 X 6C1

Add the latter two results and divide by the total number of ways to get .82