A or B?

$\dfrac{A}{B} = \dfrac{64!}{60} \times \dfrac{64 \times 61}{65!} = \dfrac{64!}{65 \times 64!} \times \dfrac{64 \times 61}{60} = \dfrac{64 \times 61}{65 \times 60} = \dfrac{64 \times (60 + 1)}{(64 + 1) \times 60} = \dfrac{64 \times 60 + 64}{64 \times 60 + 60} > 1 \Rightarrow \boxed{A > B}$

Factor out 59! from both and cancel denominators.

A = 64x63x62x61 = 15249024

B = 65x63x62x60 = 15233400

A>B

65! is 65 times bigger than 64! and 64x61=3904, 3904:60 is slightly bigger than 65

We can write $\frac{64!}{60}$ as $\frac{65!}{65×60}$ .

And, $\frac{65!}{65×60}$ > $\frac{65!}{61×64}$

$\Rightarrow$ $\frac{65!}{3900}$ > $\frac{65!}{3904}$

So, $\boxed{A>B}$