Discrete Math Question

discrete math practice test / quiz and need the explanation and answer to help me learn.

Just show the work and answer
Requirements: solution and answer
MATH 243 Q U I Z 9 You may leave calculations set up without multiplying out 1. Suppose product codes are made up of 4 uppercase letters (A – Z), followed by 3 digits (0 – 9), and then followed by 2 more uppercase letters. How many product codes can be made using the system above if: a. there are no restrictions? b. there are no even digits? c. there is at least 1 even digit? 2. How many bitstrings of length 14 a. begin with 001? b. begin and end with 001? c. begin or end with 001? 3. Nine people need to line up for a photograph. How many different ways can you line up those nine people: a. if there are no restrictions? b. if the tallest person has to go last? c. if the tallest person has to be immediately to the left of the 2nd tallest? 4. A deck of cards for a game has 20 orange cards, 35 yellow cards, 25 green cards, 30 pink cards and 35 white cards. What is the minimum number of cards you would have to pick to guarantee you had: a. 15 cards of the same color? b. 15 pink cards? 5. A store sells 50 different types of snacks. How many ways can you choose 8 different snacks to buy if: a. you give all 8 snacks to the same person? b. you give each of the 8 snacks to a different person? 6. A class has 30 students: 20 computer science majors and 10 math majors. The teacher wants to form a group of 4 students to work on a project together. How many groups of 4 students can they form if: a. any 4 students can be chosen? b. there must be 3 computer science major and 1 math major? c. there must be at least 1 computer science major?

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