(1) How many ways can the letters of the word DRAGONFLY be arranged in a row? (2) How many ways can the letters of the word DRAGONFLY be arranged if the letters FLY must appear together in that order? (3) How many ways can the letters of the word DRAGONFLY be arranged if the letters FLY must appear together but may be in any order? (Please enter each of your answers as an integer without comma or period.)  

(3 points for the correct answer. 1 bonus point if you have correctly answered Questions 1 through 5.) A survey was conducted in a class of 50 students regarding the math and computer science courses they had taken prior to the current class. The results are as follows: (1) 30 students took Precalculus, (2) 18 students took Calculus, (3) 26 students took Data Mining, (4) 9 students took both Precalculus and Calculus, (5) 16 students took both Precalculus and Data Mining, (6) 47 students took at least one of the three courses, (7) 6 students took all three courses. How many students took both Calculus and Data mining? Hint: Consider the inclusion/exclusion rule for three sets: If A, B, and C are any finite sets, then    

(3 points for the correct answer. 1 bonus point if you have correctly answered Questions 1 through 5.) A survey was conducted in a class of 50 students regarding the math and computer science courses they had taken prior to the current class. The results are as follows: (1) 30 students took Precalculus, (2) 18 students took Calculus, (3) 26 students took Data Mining, (4) 9 students took both Precalculus and Calculus, (5) 11 students took both Calculus and Data Mining, (6) 47 students took at least one of the three courses, (7) 7 students took all three courses. How many students took both Precalculus and Data Mining? Hint: Consider the inclusion/exclusion rule for three sets: If A, B, and C are any finite sets, then     

An identifier consists of 2 letters chosen from {m, n, p, r, s} followed by 3 digits from 0–9.  (1) How many identifiers are possible if letters and digits may repeat? (2) How many identifiers are possible if letters may repeat but digits may not repeat? (3) How many identifiers containing at least one repeated letter or repeated digit? (Please fill each blank with an integer and without comma or period.)

A bit string is a finite sequence of 0’s and 1’s. (1) How many bit strings have length 9? (2) How many bit strings of length 9 begin with four zeros? (3) How many bit strings of length 9 begin with 1 and end with two ones? (Please fill each blank with an integer and without commas or periods.) 

What should Trendy’s optimal order size be to start the first half of the season?

What is Trendy’s expected profit for the first half of the season?

____ states that socialization teaches people how to behave in any given situation.

The nurse identifies cephalopelvic disproportion (CPD) in a laboring patient. Which “P” of labor does this primarily involve?

Pressure, pain, and temperature receptors in the skin are ____.