How many seats in this auditorium 2 2 0 1 2 1 3 4 5 6 1 n i 1 0 7 8 1 7 1 8 1 6 i 1 6 7 6 7 5 7 1 1 9 5 5 5 5 8 1 7 8 1 5 5 8 1 1 75 7 78 7 1 7 1 1 1 1 1 1 1 3 4 3 4 2 3 4 7 2 1 3 4 3 4 2 3 4 7 2 1 There Exists For Every A 1 B A B A B A B 30 A A 4 B 2 1 2 1 It s one of the most important mathematic al ideas of all time B C 5 1 1 6 C 7 D 6 1 The empty set is a set with all the rights and privileges pertaining thereto B E F A A B C 7 5 7 56 5 5 3 4 7 6 G 6 6 7 6 6 5 5 3 4 7 3 4 G C 1 7 3 4 C 1 5 5 3 4 7 H 6 G 6 6 7 I1 8 J 8 7 8 7 1 3 6 4 7 1 The number of subsets of an n element set n is 2 I own 3 beanies and 2 ties How many different ways can I dress up in a beanie and a tie 2 K 5 6 3 7 21 5 6 3 7 630 5 1 2 K 6 7 4 8 1344 5 1 1 6 C 0 0 0 1 1 1 0 0 1 L 0 0 1 1 0 A 1 1 C 0 0 0 1 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 M M 6 M 1 1 0 1 0 1 A A 4 4 L 8 1 N 56 1 0 0 C 1 0 4 4 C 0 N O C N 56 0 1 8 L 0 Ordering of a deck C 8 8 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 8 P P P6P5P A P 7 0 0 1 0 C K K C K K P P P 5P P P 0 B 0 B1 3 4 P H I 1L 7 H P G 3 4 I 3 4 P H I 1L 9 7 2 3 4 P 0 0 Q H 1O A I A 7 L 9 Q 0 2 1 0 AB 1 B3 4 Q H IL B B 7 H Q G B3 4I 7 H P G 3 4 B3 4 I1 3 B4 7H Q 7 H P G 3 4 B G B3 4I B3 4 I1 93 B4 7 9 Q 9B 0 B 9B B F N R 9 Q 93 B4 1 1 P PS7K 0 1 111 P 3 4 P 3 4 P6P 3 3 44 7 3 4 F 8 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 8 C 52 51 50 49 48 5 52 51 50 49 48 5 2 598 960 0 3 0 0 4 1 3 4 The number of subsets of size r that can be formed from an n element set is 3 4 S C S K 0 C 0 1 S 4 1 S 4 1 C 1 S S S 1 3 4 5 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 5 5 4 4 ways of picking 3 of the 4 aces 3 48 1128 ways of picking 2 cards non ace cards 2 4 1128 4512 4 1 way of picking 4 of the 4 aces 4 48 ways of picking one of the remaining cards S 7 4704 4560 At least one of the two counting arguments is not correct C 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 E E E E Is the other argument correct How do I avoid fallacious reasoning 3 4 0 C 1 4 4 5 E 1 E E E E Is the other argument correct How do I avoid fallacious reasoning 4 4 5 B E 1 4 4 E 1 A B A 14 6 B A route is any sequence containing 6 D s and 8 R s
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