Brooklyn College MDM4U

Name: ______Due Date: ______

Mathematics of Data Management

Chapter 5Assignment - Combinations and the Binomial Theorem

KU / APP / COM / TIPS / Total
24 / 22 / 4 / 4 / 54

Part A – Knowledge and Understanding

  1. [10] Given the following sets:

A = {♠, ♥, ♣, ♦, ©, ®}

B = {♠, ♥, ©, ♣, ☺}

C = {♫, ☼}

a)List the elements in the universal set S. ✓

b)Determine n(A B). ✓

c)List the elements in B C. ✓

d)Determine n (A C B). ✓

e)Is it possible to intersect two sets above that will result in the null set? Explain. ✓✓

f)How many total subsets can you make from set S, the universal set? ✓

g)How many subsets of size 2 or 3 can you make from set A B? Express in combination form and evaluate. ✓

h)Draw a Venn Diagram for the sets A, B and C. ✓✓

  1. [1] There are 22 terms in the expansion of . What is the value of n?
  1. [1] What is the first term of the binomial expansion in Question #2 above?
  1. [1] Using your knowledge of Pascal’s Triangle, what combination is equal to ?
  1. [1] Kyle was writing a geography test. There were 21 questions on the test and he was required to answer exactly 10 of them. The first 4 and the last 2 questions were mandatory. How many different sets of questions could Kyle choose to answer? Explain. (1 mark)
  1. [1] How many different sums of money can you make with two loonies, two $5 bills, one $20 bill and four $50 bills?
  1. [1] How many ways can you line seven students out of 10 to pose for a picture?
  1. [1] How many ways can you select a group of seven students from a group of 10 to decorate the classroom?
  1. [2] There are 21 students available to be selected at random to form a committee of six. How many different committees can be formed if Casey, Vanessa and Erika must be on the committee?
  1. [2] A term in the expansion of is 1451520. What is the value of m?
  1. [3] Expand the first four terms of:

Part B – Applications

  1. [8] The Hawks Hockey team has 12 forwards, 7 defensemen and 2 goalies.

a)Use combinations to determine the number of different ways Coach Waterhouse can select six players to sing Oh Canada at the yearend assembly. ✓

b)Use combinations to determine the number of ways coach Waterhouse can select his starting lineup if he must select three forwards, two defensemen and Troy, the team’s #1 goalie. ✓✓

c)How many of these starting line ups include Troy, the team’s #1 goalie and Alastair, the team’s #1 forward? ✓

d)How many starting line ups are possible if the forwards are allowed to play the defense position also?✓✓

e)For today’s championship game, forward Jack, forward Ethan, defenseman Erik and defenseman Nikolas cannot play due to illness. Fortunately, the 5 healthy defensemen can also play the forward position. How many starting line-ups can Coach Waterhouse make under this scenario? ✓✓

  1. [3] From a deck of 52 cards, how many different four card hands could be dealt which include at least one heart? Show two ways to arrive at your answer.
  1. [2] There are 15 girls on Highland’s volleyball team, 18 girls on the basketball team and seven girls who play on both teams. Use a Venn diagram and use the principle of inclusion and exclusion to illustrate this situation and determine how total many girls are involved on both teams.
  1. [5] Out of a survey of 42 grade ten students at Highland, 16 played soccer, 14 played hockey and 13 played basketball; Of the total surveyed, 5 played both basketball and hockey; 7 played soccer and basketball and 6 played soccer and hockey. Four students played all three of the sports.

a)Use a Venn diagram to organize this data. ✓✓

b)How many of the surveyed students play at exactly one of the three games? ✓

c)How many of these students play at least two of the games? ✓

d)Determine n(basketball hockey). ✓

  1. [1] The 21 members Highland mathematics club had a party at lunch yesterday. Each person shook hands with everyone who was present once. How many total handshakes were there?
  1. [3] A committee of five athletes is to be selected at random from 10 hockey players and 12 football players. How many different committees are possible that include at least three football players?

Part C – Communications

  1. [4] Explain why 4 objects have more permutations than combinations. Use a Simple example to illustrate your explanation. By what factor is one larger than the other?

Part D – Thinking, Inquiry and Problem Solving

  1. [4] In poker, you are dealt five cards for your hand. Determine the number of ways you can get a “three of a kind”. (a poker hand such as 2♦ 2♠ 2♣ K♠ 6♥ that contains three cards of the same rank, plus two cards which are not of this rank nor the same as each other) How would it change of you were playing with a seven card hand? Explain your solution.

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