Compute the following values and show how you got your answers: a)The number of

Question

Compute the following values and show how you got your answers: a)The number of 5-card hands that contain two pairs from a 52-card deck. b)The number of 2-elements subsets from the set {1, 2,...,200} where the sum of the two elements is even. Suppose you are playing Mastermind and give the following guesses and get the stated results. What is the code? Guess Result G R Y P 3 correct in correct places R Y P B 2 correct in wrong places G R Y O 2 correct in correct places, 1 correct in wrong place G O Y P 2 correct in correct places, 1 correct in wrong place A professor has 12 students in his graduate class. Each student will receive a grade of A or B. a)In how many ways can the professor assign grades? b)How many different grade distributions are possible? (Everyone getting an A is one distribution. Everyone getting a B is another. c)How many ways could 5 students get A and the rest get B?

Explanation / Answer

I will only answer all parts of first question here. Please ask the rest seperately.

Compute the following values and show how you got the answers.

a) The number of 5 card hands that contains 2 pairs from a 52-card deck.

A pair is when 2 cards of same denomination are present (say a 2 of spades and a 2 of hearts). There are a total of 13 denominations. Since we have to choose 2 pairs first we have to choose 2 denominations out of 13 and then within each 2 cards out of 4 suits.This accounts for 4 of the cards. Now to select the last card we have to keep in mind that it does not belong to the two denominations that have been already selected before. There are 44 options still available out of which one card has to be selected. Thus the required number will be given by,

N = C(13,2)*C(4,2)*C(44,1) = 20,592

b)

There only two ways the sum of two numbers can be even. Either both of the number are even or both of the number are odd. There are 50 even and 50 odd numbers in the set. The total number of ways should consist of sum of choosing two even numbers out of 50 and 2 odd numbers out of 50 odd numbers.

Thus the required number will be given by,

N = C(50,2) + C(50,2) = 2,450

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.