Question

Winning the jackpot in a particular lottery requires that you select the correct three numbers between 1 and 53 ​and, in a separate​ drawing, you must also select the correct single number between 1 and 45. Find the probability of winning the jackpot.

Answer 1

$|\Omega|={_{53}C_3}\cdot 45=\dfrac{53!}{3!50!}\cdot45=\dfrac{51\cdot52\cdot53}{2\cdot3}\cdot45=1054170\\|A|=1\\\\P(A)=\dfrac{1}{1054170}\approx0.00000095\%$