Discrete Structures 2: Counting Principles and Arguments

GENERAL INSTRUCTIONS: Answer the following problems neatly and correctly. Show your solution and box your nal answer. Probleml. You are creating a 4digit pin code. How many choices are there in the following cases? (a) With no restriction. (3 points) (b) No digit is repeated. (3 points) ((2) No digit is repeated, digit number 3 is a 0. (3 points) (:1) No digit is repeated, and they must appear in increasing order. (3 points) (e) No digit is repeated, 2 and 5 must be present. (3 points) Problemz. You a How many different words can be created by rearranging the lettersin SELFIESTICK? (5 points) Problem3. We have four different dishes, two dishes of each type. In how many ways can these be distributed among 8 people? (5 points) Problem4. How many words can you create of length 6, from the letters a, b, c and d if: (a) you must include each letter at least once, and (5 points) (b) \"a\" must appear exactly once. (5 points) Problems. We have four different dishes, two dishes of each type. In how many ways can these be distributed among 3 people? (5 points)