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Math
A First Course in Probability
Chapter 1
Q.1.5 - Theoretical Exercises

A First Course in Probability

Sheldon M. Ross

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 432 pages

ISBN: 9780321794772

Chapter 1: Q.1.5 - Theoretical Exercises (page 17)

Determine the number of vectors $(x_{1}, . . . x_{n)}$ such that each $x i$ is either $0$ or $1$ and
${鈭�}_{i = 1}^{n} x_{i} 鈮� k$

Short Answer

Expert verified

The number of vectors $(x_{1}, . . . . . x_{n})$ is $144 a n d 18$

Step by step solution

01

Step-1 Given Information

Given in the question that,

Code is sequence of $3$ digits

The first digit is an integer between $2 a n d 9$

Second digit is either $0 o r 1$

Third digit is integer between $1 a n d 9$

we have to find the number of vectors.

02

Step-2 Explanation

Case (a): $3$ digit code

First digit $= 8$ options $(2 - 9)$

Second digit $= 0 o r 1 (2 o p t i o n s)$

Third digit $= 9$ options $(1 - 9)$

Total number of possible area codes will be

localid="1650010466242" $= 8 脳 2 脳 9 = 144$

Case (b):

First digit $= 1$ options $(4)$

Second digit $= 0 o r 1 (2 o p t i o n s)$

Third digit $= 9$ options $(1 - 9)$

Total number of possible area codes will be

localid="1650010663142" $= 1 脳 2 脳 9 = 18$

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Most popular questions from this chapter

Five separate awards (best scholarship, best leadership qualities, and so on) are to be presented to selected students

from a class of $30$ . How many different outcomes are possible if

(a) a student can receive any number of awards?

(b) each student can receive at most $1$ award?

Determine the number of vectors $(x_{1}, . . ., x_{n})$ such that each $x_{i}$ is a positive integer and

role="math" localid="1649161391681" ${鈭�}_{i = 1}^{n} x_{i} 鈮� k$

where $k 鈮� n$ .

How many $5$ -card poker hands are there?

There are $(\begin{matrix} n \\ r \end{matrix})$ different linear arrangements of $n$ balls that $r$ are black and $n 鈭� r$ are white. Give a combinatorial explanation of this fact.

Suppose that $10$ fish are caught at a lake that contains $5$ distinct types of fish.

$(a)$ How many different outcomes are possible, where an outcome specifies the numbers of caught fish of each of the $5$ types?

$(b)$ How many outcomes are possible when $3$ the $10$ fish caught are trout?

$(c)$ How many when at least $2$ of the $10$ are trout?

See all solutions

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