CSCI 2405
Discrete Mathematics II
Fall 2017
Homework Assignment 2

Due: Monday, September 11, at the beginning of class.

  1. Suppose that you roll two dice, one red and one blue. Each die has 6 possible outcomes: 1, 2, 3, 4, 5 or 6. There are 36 possible combined outcomes for the two dice. For each of the following conditions, say how many of those 36 outcomes satisfies the condition.

    1. The red die shows 3.
    2. At least one of the dice shows 3.
    3. The sum of the dice is 4.
    4. The sum of the dice is less than 5.
    5. The two dice show the same value.

  2. For Mother's day, Eloise's daughter always sends her either a balloon or a flower arrangement from lastminutegifts.com, which offers 10 different balloons and 45 different flower arrangements. How many different gifts can Eloise receive?

  3. Suppose that Eloise receives both a balloon and a flower arrangement. How many combined gifts can Eloise receive?

  4. A regular Massachusetts license plate can have two forms. One form consists of 3 digits followed by 3 letters. The other form consists of 4 digits followed by 2 letters. There are 10 digits and 26 letters. How many different regular Massachusetts license plates are there?

  5. At State University, many students are majoring in two or more subjects. In all, there are 320 computer science majors, 145 math majors and 580 business majors. There are 35 students majoring in both computer science and math, 20 students majoring in business and math, 90 students majoring in business and computer science, and 10 students majoring in all three.

    Students majoring in two or three majors are counted in the total for both majors. For example, the 35 students majoring in both computer science and math are among the 320 computer science majors and the 145 math majors.

    1. How many students are majoring in computer science or math?
    2. How many students are majoring in computer science or business?
    3. How many students are majoring in computer science, business or math?

  6. The New Village Cinema shows 6 different movies in 6 different 300-seat theaters. (Each theater shows one movie, and no two theaters show the same movie.) Suppose that exactly 1111 people come to the theater on Saturday night.

    1. What is the largest value of N so that the statement "I know that at least N people will view the same movie" will surely be true.

    2. Suppose there are only five 300-seat theaters, showing five different movies. Answer the same question as part (a), again with 1111 movie viewers.

  7. Answer each of the following.

    1. In how many ways can you arrange the letters of JUPITER, using all of the letters?

    2. How many 5-letter strings can you make using only the letters in JUPITER if all 5 letters must be different?

    3. How many sets of 5 different letters can you choose from the letters of JUPITER?

  8. A poker hand consists of 5 cards drawn from a deck of 52 cards.

    1. How many different poker hands are there?

    2. How many hands are there that contain the ace of spades?

    3. There are 4 aces in the deck. How many hands include all four aces?

    4. There are 12 face cards in the deck. How many hands contain only face cards?

      5.