The question is:
In LOTTO $49$, Michigan’s lottery game, a player selects $6$ integers out of the first $49$ positive integers. The state then randomly selects $6$ out of the first $49$ integers. Cash prizes are given to a player who matches $4, 5$, or $6$ integers. Let $X$ be the number of integers selected by a player that match integers selected by the state. Find $P(X = 1)$.
The answer is: $.413$
I'm not sure where to start. I thought about doing ${49 \choose 6}$ to represent the numbers the state chooses. But I'm not sure what do from there to see what the probability is that a player chooses exactly $1$ integer that matches.
$6$ numbers are lucky numbers, $43$ of them are not.
Hence $$P(X=1)=\frac{\binom{6}{1}\binom{43}{5}}{\binom{49}{6}}.$$