>>2341660//before i start, keep in mind that I'm usually shit at math
•the probability of drawing one card and getting A is 3/60
•therefore probability of drawing 5 cards and getting all letters, in specific order is (3/60)^5
•however we don't care about order so we multiple this with total number of qays you can arrange five cards which is 5!
•therefore, drawing five cards and getting all letters has probability = 5!*(3/60)^5
•now, there are 35 other cards you've pulled out and we don't care what they are, so we multiple the total number of ways you can choose 35 cards from 55 cards
55C35 = 55!/35!*20!
•therefore, total probability of drawing forty cards and getting one of each letter is {3^5 * 5! * 55!} / {35! * 20! * 60^5}
if you calculate that, you should get the right answer.
I'm just an engineering fresher though, so I'm pretty sure there are far better sources here
