Unformatted text preview: Headcounting: 40C, 35E, 30M, 25P. (a) There are 4 patterns: { C,E,M } , { C,E,P } , { C,M,P } , { E,M,P } . Then 40 Â· 35 Â· 30 + 40 Â· 35 Â· 25 + 40 Â· 30 Â· 25 + 35 Â· 30 Â· 25 = 133250 . (b) Consider the complement: if all three members are from the same department, there are Â± 40 3 Â² + Â± 35 3 Â² + Â± 30 3 Â² + Â± 25 3 Â² = 22785 choices. The number of choices without any restriction is Â± 40 + 35 + 30 + 25 3 Â² = 357760 . Thus the answer for this part is 35776022785 = 334975 . (c) There are two patterns: { C,M,P } , { E,M,P } . The answer is 40 Â· 30 Â· 25 + 35 Â· 30 Â· 25 = 56250 . 5. Consider the complement : passwords that contain no digit or no letter, in other words, contain only letters or digits. There are 5 6 = 15625 passwords that contain only letters. Similarly, there are also 15625 passwords that contain only digits. The total number of passwords is 10 6 . Thus our answer is 10 62 Â· 15625 = 968750 . 1...
View
Full Document
 Spring '07
 Graham
 Algorithms, Patterns, Harshad number, Numerical digit, total number, Consonant

Click to edit the document details