Discrete Mathematics Answers

. A special type of password consists of six(6) different letters of the alphabet, where each letter is used only once. How

many different possible passwords are there? (3 pts)

A. 244, 140, 625

B. 308, 915, 776

C. 165,765,600

D. 213,127,200 

A. COUNTING METHODS (5 pts each)

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. (10 pts)

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? 

If P(k) = k2

(k + 2)(k – 1) is true, then what is P (k + 1)? 

At a college of 600 students there are (n+5) enrolled in physics, (n+20) in Mathematics who play sports and (n-15) in chemistry and play sports. Create a Venn diagram to illustrate this information. Where n=8

At a college of 600 students there are (n+5) enrolled in physics, (n+20) in Mathematics who play sports and (n-15) in chemistry and play sports. Create a Venn diagram to illustrate this information. Where n is your arid number.

At a college of 600 students there are (n+5) enrolled in physics, (n+20) in Mathematics who play sports and (n-15) in chemistry and play sports. Create a Venn diagram to illustrate this information. Where n=8

At a college of 600 students there are (n+5) enrolled in physics, (n+20) in Mathematics who play sports and (n-15) in chemistry and play sports. Create a Venn diagram to illustrate this information. Where n is your arid number

There are 18 325 Computer and 415 English majors at colege . ( a ) How many ways to pick 5 math 125 computer and 300 English majors ? many ways to pick one Yepresenta tative who is either Math or computer . Eng / i * s * h ? ( 6 ) How

A survey was given to 140 students. On average, 2 out of 7 students floss every day. How many students do NOT floss every day?

Write down the mathematical notations for The set of all natural number whose square is more than 21.