## Combinatorics Assignment 2016

Question
Combinatorics Assignment

WORLDATLAS.COMThe flag of GabonA lot of national flags are made up of three horizontal stripes.
How many different three colour flags(tricolors)can be designed using green, blue, red, yellow and black stripes if all three colours must be different?
How many of them contain a red stripe?
How many extra possibilities are there if the top colour can be the same as the bottom colour?
3 marks
On his university application, Prashad must list his course choices in order of preference.He must choose four of the six courses available in his major discipline and three of the four courses offered in related subjects.In how many ways can Prashad list his course choices? Explain the reasoning for your answer.5 marks
Idi is creating a password for a website that has some strict requirements. The password must be 8 characters. Numbers and letters may be used, but may not be repeated.
How many different passwords are possible?
How many are possible if the following restrictions are enforced;

The password must feature both numbers and letters?
8 marksMarissa is doing a Tarot reading in which she must pick 6 cards from a deck of 72. The order of their selection is not important.
How many different readings are possible?
Marissa does not want to see the Fool card. There is one Fool card in the deck. How many of the possible readings do not feature the Fool card?
5 marksA committee of 5 people is to be chosen from a group of 8 women and 10 men.
How many diffferent committees are possible?
How many are possible if the following restrictions are enforced;

The committee must feature both men and women? The committee must feature 3 women and two men? The committee must have more women than men?8 marksA baseball team has 14 players.LATIMES.COMBaseball at the Summer OlympicsNate Schierholtz (R) of the US barrells into Chinese catcher Yang Yang (L) to score off a hit by Terry Tiffee in their men’s preliminary round baseball game at the Wukesong Baseball Venue during the 2008 Beijing Olympic Games on August 18, 2008. The US won 9-1.
How many 9-person batting orders are possible?
How many batting orders are possible if Schierholtz is always in the starting line-up and always bats fourth?
4 marksConsider the word MATHEMATICS.
How many arrangements are there of the word MATHEMATICS?
How many of the arrangements in part a have the T’s together?
6 marksWe have looked at situations in which we need to determine the number of possible routes between two places. We can look at the situation below as 9 steps, six of which must be East and three of which must be South.
.909px;=”” collapse;=”” 12px=””>
This gives us 9! = 84 possible routes
3!6!

.909px;=”” collapse;=”” 12px=””>
The calculation 9! is equivalent to 9C3 (or 9C6)
3!6!
Explain clearly why you could solve this question using combinations, and why this is equivalent to considering permutations with repeated items.
4 marks
There are 8 parents and 43 students going on a school trip. Two groups are made, a large one with thirty students and five parents, and a small group with 13 students and three parents.
How many different ways can be the parents be chosen for the small group?
How many ways can the students be chosen for the large group if Stefan and Dylan must be in the small group?
How many ways can the groups be arranged if Reena and both her parents must be in the small group?
6 marksSimplify each expression and write it without using factorial notation.
(n + 4)!
(n + 2)!
(n ? r + 1)!
(n ? r ? 2)!

6 marksInvestigate a lottery competition somewhere in the world. Explain how the lottery works, and what needs to happen for someone to win the jackpot, and at least one of the minor prizes.DAILYRECORD.CO.UKLottery BallsCalculate the probability of winning each of the prizes you described, giving a full explanation of your work.
Consider the cost of playing. Do you think the prizes offered are fair? If not, why not, and why do you think people continue to play?