Answer to Question #190418 in Discrete Mathematics for Angelie Suarez

Question

A. COUNTING METHODS

1. How many strings of length 4 can be formed using the letters ABCDE if it starts with letters AC and repetition is not

allowed?

2. There are 10 multiple choice questions in an examination. Each of the questions have four choices. In how many ways

can an examinee give possible answers?

B. BINOMIAL COEFFICIENTS

Expand (2𝑥 + 4𝑎) 4 using the binomial theorem.

C. PIGEONHOLE PRINCIPLE (5 pts) . Explain briefly.

Do you agree that there are 3 persons who have the same first and last name? Why and why not? 

Answer 1

(A)

1.Number of ways in which 4 length string formed when first two words are $AC= 1\times ^3C_2=3$

2.Number of ways in which examinee fives possible answer$= 4^{10}$

(B)

Given expression-

$(2x+4a)^4\\[9pt] =^4C_0(2x)^0(4a)^4+^4C_1(2x)^1(4a)^3+^4C_2(2x)^2(4a)^2+^4C_3(2x)^3(4a)^1+^4C_4(2x)^4(4a)^0 \\[9pt]=256a^4+512xa^3+384a^2x^2+32x^3a+46x^4$

(C) Yes, we can say that number of person who have the same first and last name is 3.