Discrete Mathematics Answers

a) In how many ways can a committee of 5 be chosen from 9 people?

(b) How many committees of 5 or more can be chosen from 9 people?

(c) In how many ways can a committee of 5 teachers and 4 students be chosen

from 9 teachers and 15 students?

(d) In how many ways can the committee in (C) be formed if teacher A refuses

to serve if student B is on the committee?

bit is either 0 or 1: a byte is a sequence of 8 bits. Find

(a) the number of bytes that can be formed

(b) the number of bytes that begin with 11 and end with 11

(c) the number of bytes that begin with 11 and do not end with 11 and

(d) the number of bytes that begin with 11 or end with 11.

Find the expansion of

a) (x + y)^6

b) (x + y)^4

31) What is the coefficient of x^12 y^13 in the expansion of (x + y)^25?

32) What is the coefficient of x9 in (2 − x)19?

33) What is the coefficient of x^101 y^99 in the expansion of (2x − 3y)^200?

Use the binomial theorem to find the coefficient of x^a y^b in the expansion of (2x^3

− 4y^2)

7, where

a) a = 9, b = 8.

b) a = 8, b = 9.

c) a = 0, b = 14.

d) a = 12, b = 6.

e) a = 18, b = 2.

35) How many unique partitions of the word ARKANSAS are there?

36) A group of six students consists of 3 seniors, 2 juniors, and 1 sophomore. How

many unique partitions of this group of students are there by grade?

Out of a group of ten residents in a certain county, 3 are Republicans, 5 are

Democrats, and 2 are Independents. How many unique partitions of this group

of residents are there by political party?

38) You have eight distinct pieces of food. You want to choose three for breakfast,

two for lunch, and three for dinner. How many ways to do that?

39) You teach a class with 90 students. In a rather severe effort to combat grade

inflation, your department chair insists that you assign the students exactly 10

A’s, 20 B’s, 30 C’s, 20 D’s, and 10 F’s. How many ways to do this?

40) How many 13-card bridge hands have 4 of one suit, 3 of one suit, 5 of one suit, 1

of one suit?

multiple-choice test contains 10 questions. There are four possible answers for each question. a) In how many ways can a student answer the questions on the test if the student answers every question? b) In how many ways can a student answer the questions on the test if the student can leave answers blank?

[T] Find "\\mathbb{Q}\\cup \\mathbb{N}" ?

R= {(1,3) ,(1,4) , (3,2) , (3,3), (3,4)} on A={1,2,3,4}