0 3 0 3 1 3 02 0 0 2 4 5 6 7 2 n i 1 1 8 9 2 8 2 8 2 9 2 6 i 1 6 8 6 8 6 8 2 2 6 6 6 6 9 2 8 9 2 6 6 9 2 2 8 9 86 8 8 2 8 2 2 2 2 2 2 2 0 4 5 4 5 3 0 4 5 8 3 02 0 4 5 4 5 3 0 4 5 8 3 02 2 0 0 0 0 0 0 41 A 5 3 2 3 2 B C 6 222 7 C 8 D 7 2 B E F A A B 9 C 4 A 5 8 6 7 8 67 6 4 5 8 6 7 7 G 8 6 6 4 5 8 4 5 G 8 C 7 7 2 C 4 5 2 6 4 5 8 H 7 6 7 7 G 8 I2 9 8 9 J 9 8 2 4 7 5 8 2 0 4 5 4 5 3 0 4 5 8 3 02 3 0 9 3 0 0 2 2 4 583 9 2 2 4 583 02 3 K 5 6 3 7 21 5 6 3 7 630 6 2 3 K 6 2 6 7 4 8 1344 3 2 H 2 3 L M I 7 2 C N 1 A 2 C 1 2 O O 7 O 1 2 A A 5 5P N 9 2 P 67 1 2 1 C 2 5 C 1 P M 5P 1 C P 67 1 2 9 N 1 Ordering of a deck C 9 9 52 possible choices for the first card 51 possible choices for the second card 50 possible choices for the third card 1 possible choice for the 52cond card 9 0 Q Q Q7Q6Q A Q 8 1 1 1 2 C K K C K Q Q Q 6Q K Q Q 1 1 B B2 4 5 Q H 2 N N 0 1 0 0 3 I 8 H Q G 4 5 I A 4 1 8 3 0 0 5 1 M B 1 B4 5 0 H I B4 5 4 5J 0 P H B4 5 I B 8 4 B5 1 B 1 B 8 0 4 B5 2 2 QR QS8K 1 2 222 Q 4 5 Q 4 5 Q7Q 4 4 55 8 4 5 F 9 52 51 52 51 2 divide by overcount Each unordered pair is listed twice on a list of the ordered pairs but we consider the ordered pairs to be the same F 9 52 51 52 51 2 divide by overcount We have a 2 to 1 map from ordered pairs to unordered pairs Hence the unordered pairs ordered pairs 2 F 9 C 52 51 50 49 48 5 52 51 50 49 48 5 2 598 960 1 4 1 1 5 2 4 5 4 5 S C S K F 1 1 C 2 S 5 2 S 5 2 C 2 S S S 2 4 5 6 4 3 49 2 4 ways of picking 3 of the 4 aces 1176 ways of picking 2 cards from the remaining 49 cards 4 1176 4704 6 4 3 48 2 6 4 ways of picking 3 of the 4 aces 1128 ways of picking 2 cards non ace cards 4 1128 4512 4 4 1 way of picking 4 of the 4 aces 48 ways of picking one of the remaining cards S 8 0 12 C 4 3 4 ways of picking 3 of the 4 aces 49 1176 ways of picking 2 cards from the remaining 49 cards 2 4 1176 4704 E E E E 4 5 1 C 2 5 5 6 E 2 E E E E 5 5 6 B E 2 5 5 E 2 T T T 3 T T0 0 P A
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