Since the cards are drawn one after the other without replacement from a well shuffled pack of cards untill an ace card appears. Then the probability that exactly 5 cards are drawn before the first ace card appears =
48
52
×
47
51
×
46
50
×
45
49
×
44
48
×
4
47
=
4
49
[
46×45×44
52×51×50
]=
4
49
(
11×23×3
13×17×5
)
=
4
49
(
P1⋅P2⋅P3
P4⋅P5⋅P6
), (given) where Pi is prime ∴max(pi)=23 and min{Pi}=3