Assignment:
Q1. How many ways can n books be placed on k distinguishable shelves?
a) if the books are indistinguishable copies of the same title?
b) if no two books are the same, and the positions of the books on the shelves matter?
Q2. How many ways are there to deal bands of five cards to each of six players from a deck containing 48 different cards?
Q3. How many ways are there to select three unordered elements from a set with five elements when repetition is allowed?
Q4. There are 2504 computer science students at a school. Of these, 1876 have taken a course in Java, 999 have taken a course in Linux, and 345 have taken a course in C. Further, 876 have taken courses in both Java and Linux, 231 have taken courses in both Linux and C, and 290 have taken courses in both Java and C. If 189 of these students have taken courses in Linux, Java and C, how many of these 2504 students have not taken a course in any of these three programming languages?
Provide complete and step by step solution for the question and show calculations and use formulas.