Chapter 7 - Section 7.1 - An Introduction to Discrete Probability - Exercises - Page 451: 8

47/52

There are $\binom{52}{5} = \frac{52!}{47! 5!} = 2,598,960$ possible five-card poker hands. If the queen of hearts cannot be draw, there are $\binom{51}{5} = \frac{51!}{46! 5!}$ such hands. Thus the probability is $$\frac{51!}{46!5!}\frac{47!5!}{52!} = 47/52$$