statistics lottery probability math equation

Question

Winning the jackpot in a particular lottery requires that you select the correct

four

numbers between 1 and

61

​and, in a separate​ drawing, you must also select the correct single number between 1 and

48.

Find the probability of winning the jackpot.

im a bit confused on how to do this help would be appreciated thank you!

Answer 1

Well there are 61 C 4 ways of choosing the four, and 48 ways of choosing the one, so

total number of ways of choosing the numbers is 61 C 4 multiplied by 48.

Only one way wins the jackpot so the probability = 1 / (61 C 4 x 48) = 1 / 25049040

61 c 4 = 61 ! / (4 ! 57 !) = 521855