.

CS1029/notes-2023-11-15

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+

CS1029/notes-2023-11-28

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+

CS1029/practical-2023-11-17/combinatorics

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+1. a) 5 8 7 * * = 280
+   b) 6 1 + 6 * 1 + 6 * = 258
+   c) 26 2 ^ 36 4 ^ * = 1 135 420 416
+   d) 17 3 P = 4080
+   e) 26 2 P 34 4 P * = 723 465 600
+   f) 8 5 C 11 7 C * = 18 480
+
+2. a) 8 2 C 5 2 C 3 2 C * * = 840
+   b) 8 2 C 14 4 C * = 28 028
+
+3. a) (sides + 1), or 7 for the likely indented d6
+   b) (sides_1 + sides_2), or 1 for the likely intended d6
+   c) 5
+
+4. (Assuming the unaccented latin alphabet only)
+   26 3 ^ = 17 576
+
+5. 26 2 ^ 10 4 ^ 10 2 ^ + 26 4 ^ * * = 3 120 049 337 600
+
+6. 99 50 * 1 + = 4 951
+
+7. a) 10 4 C = 210
+   b) 10 4 C 10 3 C 10 2 C 10 1 C + + + = 385
+   c) 10 4 C 10 5 C 10 6 C 10 7 C 10 8 C 10 9 C 1 + + + + + + = 848
+
+8. a) 100 4 P = 94 109 400
+   b) 99 3 P = 941 094
+   c) 99 4 P = 90 345 024
+   d) 97 4 ! * = 2 328
+
+9. a) 25 4 C = 12 650
+   b) 25 4 P = 303 600
+
+10. 3 5 ^ = 243
+
+11. 5 3 ^ 3 ! / = 20
+

CS1029/practical-2023-11-24/probability

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+01. 4 52 / = 1/13
+02. 50 100 / = 1/2
+03. 1 1 52 5 C / - = 2598959/2598960
+04. 4 1 C 52 5 C / 4 2 C 52 5 C / 4 3 C 52 5 C / 1 52 5 C / sum =  1/173264
+05.
+ a) 1 50 5 C / = 1/2118760
+ b) 1 52 5 C / = 1/2598960
+ c) 1 56 5 C / = 1/3819816
+ d) 1 60 5 C / = 1/5461512
+06.
+ a) 1 200 3 P / = 1/7880400
+ b) 1 200 / 3 ^ = 1/8000000
+07.
+ a) 1 26 ! / = 1/403291461126605635584000000
+ b) 1 26 / = 1/26
+08. 4 3 C 1 2 / 4 ^ * = 1/4
+09. 6 1 C 1 2 / 6 ^ * = 3/32
+10. 2 5 / 1 2 / * 1 3 / / = 3/5
+11. P(U|P) = P(P|U)P(U) / P(P|U)P(U) + P(P|U')P(U')
+  ) 96 % 8 % * 96 % 8 % * 1 8 % - 9 % * + / = 64/133
+12.
+ a) 8 % 98 % * 8 % 98 % * 1 8 % - 3 % * + / = 196/265
+ b) 1 196 265 / - = 69/265
+ c) 2 % 8 % * 2 % 8 % * 92 % 97 % * + / = 4/2235