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(1) This problem concerns a standard deck of 52 cards. A hand consists of 5 cards. When you approach the following, you may want to ask yourself which steps/decisions you would go through to build/construct a hand we are interested in. (a) How many hands have exactly two aces? (b) How many hands have exactly 2 diamonds and exactly 2 spades? (e) How many hands have cards from all four suits? (d) How many hands either have no diamonds or have no spades?

(1) This problem concerns a standard deck of 52 cards. A hand consists of 5 cards. When you approach the following, you may want to ask yourself which steps/decisions you would go through to build/construct a hand we are interested in. (a) How many hands have exactly two aces? (b) How many hands have exactly 2 diamonds and exactly 2 spades? (e) How many hands have cards from all four suits? (d) How many hands either have no diamonds or have no spades?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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• If the answer is something like 154 × 206, you may leave it as it is. There is no need to compute the values of these expressions. • You can always verify your answers on "smaller problems". • Remember that either or means either or or both. (1) This problem concerns a standard deck of 52 cards. A hand consists of 5 cards. When you approach the following, you may want to ask yourself which steps/decisions you would go through to build/construct a hand we are interested in. (a) How many hands have exactly two aces? (b) How many hands have exactly 2 diamonds and exactly 2 spades? (e) How many hands have cards from all four suits? (d) How many hands either have no diamonds or have no spades? (2) In this problem, we are dealing with two dimensional arrays (or matrices) that have 10 rows and 10 columns. Further, each entry in the array is 1, 2, or 3. Assume that the rows as well as columns are indexed by 1 through 10. Recall that there are 3100 such matrices. (a) In how many such matrices every row has exactly 5 ones and there are no other restrictions? (b) Imagine the matrix to be divided into 4 quadrants. In how many such matrices, in every quadrant there are exactly 10 ones and there are no other restrictions?
Transcribed Image Text:• If the answer is something like 154 × 206, you may leave it as it is. There is no need to compute the values of these expressions. • You can always verify your answers on "smaller problems". • Remember that either or means either or or both. (1) This problem concerns a standard deck of 52 cards. A hand consists of 5 cards. When you approach the following, you may want to ask yourself which steps/decisions you would go through to build/construct a hand we are interested in. (a) How many hands have exactly two aces? (b) How many hands have exactly 2 diamonds and exactly 2 spades? (e) How many hands have cards from all four suits? (d) How many hands either have no diamonds or have no spades? (2) In this problem, we are dealing with two dimensional arrays (or matrices) that have 10 rows and 10 columns. Further, each entry in the array is 1, 2, or 3. Assume that the rows as well as columns are indexed by 1 through 10. Recall that there are 3100 such matrices. (a) In how many such matrices every row has exactly 5 ones and there are no other restrictions? (b) Imagine the matrix to be divided into 4 quadrants. In how many such matrices, in every quadrant there are exactly 10 ones and there are no other restrictions?
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