0 3 1 0 3 2 3 02 0 0 4 5 6 7 2 n i 1 1 8 9 2 8 2 8 2 9 2 6 6 i 1 8 6 2 2 2 8 9 2 8 6 89 86 8 6 2 2 6 9 9 6 8 6 6 8 6 2 8 2 2 2 2 2 2 0 02 2 0 4 5 4 5 4 5 4 5 3 0 4 5 8 3 3 0 4 5 8 3 2 0 0 02 41 0 0 A 0 0 5 B 3 2 C 3 2 6 222 7 C 8 D 7 2 B B E F 8 6 7 A A 8 67 6 9 C 4 A 6 6 4 5 8 4 5 C 4 5 8 5 2 C 4 5 6 4 5 8 2 H 7 G 8 6 G 8 7 7 7 7 6 7 7 G 8 I2 9 8 9 J 9 8 2 4 7 5 8 2 0 3 0 2 2 4 583 9 3 0 0 02 4 5 4 5 3 0 4 5 8 3 02 9 2 2 4 583 3 K 6 2 5 6 3 7 21 5 6 3 7 630 3 K 6 3 2 H 6 7 4 8 1344 7 2 3 2 L M I C 0 2 0 0 0 0 0 N 1 0 A 2 0 C 0 0 0 0 0 0 0 0 0 0 0 0 O O O 2 1 A 5P 9 A 5 2 2 N 7 1 0 P 67 1 2 1 1 C 2 C 1 67 C 1 9 2 0 Q Q 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 P P M 5P C 1 N 1 Ordering of a deck 5 9 Q7Q6Q Q 8 1 1 A 1 2 C K K C K Q Q Q 6Q K Q Q 2 1 1 4 5 Q H 2 B N B2 1 M N B 3 I 8 H Q G 4 5 I A 4 1 0 1 0 0 8 3 5 0 0 1 B4 5 0 H I B4 5 4 5J 0 P H B4 5 I B 1 1 B B 8 4 B5 8 0 4 B5 QR QS8K 2 2 0 1 2 222 Q 4 5 Q 4 5 Q7Q 4 4 55 8 4 5 F 9 F 9 52 51 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 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 1 F 9 C 52 51 50 49 48 5 52 51 50 49 48 5 2 598 960 4 1 1 5 2 4 5 3 4 C S K 4 5 S F 1 C 1 2 S 5 2 S 5 2 C 2 S 2 4 5 S S 6 4 3 4 4 ways of picking 3 of the 4 aces 3 49 2 1176 ways of picking 2 cards from the remaining 49 cards 4 1176 4704 6 6 4 ways of picking 3 of the 4 aces 48 1128 ways of picking 2 cards non ace cards 2 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 C 4 3 49 0 0 2 1176 ways of picking 2 cards from the remaining 49 cards 4 1176 4704 4 ways of picking 3 of the 4 aces E E E E 4 5 1 C 5 5 6 2 E 2 E E E E 5 5 6 5 5 B E E 2 2 T T T 3 T T0 0 P A
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