4 Permutations 1. Let a \"small block cipher be a function f which maps 8-bit pl

Question

4 Permutations 1. Let a "small block cipher be a function f which maps 8-bit plaintexts m E (0,1)8 to 8-bit ciphertexts c E (0,1)8. However, function f must be 1-1 or otherwise it would be impossible to invert a block cipher, i.e. compute (using the block cipher key) the plaintext f(c) given ciphertext c. How many "small" block ciphers are there? students if each student must have a computer and computers cannot be shared? capital letters but with no repeated characters? 2. There are 10 computers and 5 students. In how many ways can computers be assigned to 3. Recall problem 1. How many 8-character passwords are there made of either lower-case or . How many 10-digit decimal strings are there in which there is no repeated digits? 5. How many 10-digit decimal strings are there in which there is no repeated digits and where 5" occurs before "6"? (By "before" I mean "anywhere before" and not "mmediately before", e.g. string (5,0, 1, 2, 3, 4, 7, 8, 9, 6) is included.) 6. How many 10-digit decimal strings are there in which there is no repeated digits and where "5" and "6" are next to each other?

Explanation / Answer

2. Number of ways in which 10 computers be assigned to 5 students = 10P5 = 10 x 9x 8x 7x 6

3. Number of lowercase letters = 26

    Number of capital letters = 26

Number of 8 character password with no repeated characters = = 52P8 = 52 x 51 x 50 x 49 x 48 x 47 x 46 x 45

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