Lottery 6/49 guess at least one number

Question

What is the probability to guess at least 1 number in Lottery 6 of 49? I tried to use binomial coefficient $\binom{6}{1}\binom{43}{5}$ divide $\binom{49}{6}$ but this gives me probability of one match number. How to tackle the problem? Thank you in advance for help.

Answer 1

What is the probability that we match none of the balls? Well, that’s $\binom{43}{6} / \binom{49}{6}$.

Now, what if that doesn’t happen? That means we match at least one of the balls, precisely what we need. The probability is then $1 - \binom{43}{6} / \binom{49}{6}$.