possible solutions 
1. 
Consider the expansion of the multinomial (m + n + p + s + v)^11. a) Determine the number of uncollected terms in the expansion of this multinomial. b) Determine the number of collected terms in the expansion of this multinomial. c) Determine the value of K for the collected term Km^4n^2pv^4 BONUS! A collected term in the expansion of the multinomial shown above has coefficient 11. How many collected terms will have that coefficient? 


2. 
Consider the word microfibrillar. a) How many unique arrangements are there for the letters in this word? b) How many ways are there to arrange the letters in the word and keep the vowels from being adjacent to one another? BONUS! Write down a legitimate Englishlanguage word that fits all the following criteria. (Webster's Unabridged, in STV 313, will be used to certify words): i) The word has no fewer that 6 letters. Justify your response. DOUBLE BONUS!! Determine the maximum number of letters for a word that meets all the following conditions: i) There are at least 4 unique letters in the word. Justify your response. 


3. 
Joannie Jorgensen volunteers at the downtown Senior Citizen Center. She's responsible for keeping records and reporting statistics that describe each day's luncheon clientele. She records the following information for each diner: • the gender of the diner Last Friday, Joannie reported information about the day's luncheon diners. Here's the beginning of her report: DINER REPORT FOR FRIDAY 57 diners in all: a) How many different descriptions are possible for diners according to the records kept by Joannie? b) Yesterday there were 38 diners. How many different reports, similar to the one above, could have been filed by Joannie yesterday, given that some descriptions may have had no diners, such as the third entry in the example? 


4. 
Two octopi took part in a friendly tentacletotentacle wrestling match. Each managed to pin 4 of its opponent's tentacles with 4 of its own. In how many ways could the match have taken place? 


5. 
5. Fifty tickets, numbered consecutively from 1 to 50, are placed in a #2 mayonnaise jar on Funk & Wagnall's porch. Two tickets are drawn from the jar. The order the two tickets are drawn is not important. a) Verify that there are 1225 ways for this to occur. Explain your verification. b) Of the 1225 possible pairs of tickets, how many pairs show two numbers whose difference is 10 or less? 


6. 
Here is a problem situation and the work submitted by a student:
Analyze the student's work. Is it correct? If so, identify the key step or steps in the student's solution. If the work is incorrect, identify the error or errors in the student's work and suggest what should have been done. 
