What is the probability of getting 0 queens after drawing 7 cards?

Question

Standard 52 card deck with 4 queens.

Answer 1

52 cards, 4 queens, 7 draws

1st draw 48/52 chance of no queen

2nd draw 47/51 chance of no queen

3rd draw 46/50

4th 45/49

5h 44/48

6th 43/47

7th 42/46

chance of no queens in 7 draws is the product of all 7 above

48/52 x 47/51 x 46/50 x 45/49 x 44/48 x 43/47 x 42/46

= 48(47)(46)(45)(44)(43)(42)/(52)(51)(50)(49)(48)(47)(46)

= 45(44)(43)42/52(51)(50)(49)

= 4257/7735

= about .55

= about 55% chance of no queens in 7 draws