In this assignment you are going to focus on:Combinations and Pascal's Triangle.

Part A (Putting the Concepts to Work):

For each question you are asked to:

a) identify the information given in the question.

b) determine the appropriate formula.

c) substitute the values given into the formula and find the solution.

1. What is the number of subsets of a set containing 10 elements?

A 19 C 20

B 1024 D 1023

2. John has a $2, $1, $0.50, $0.25, $0.10, and $0.05 coin in his pocket. How many different sums of money can he make?

A 63 C 6

B 64 D 720

3. How many ways can at least two people be selected from a group of 10 people?

A 2¹⁰ - ₁₀C₀ - ₁₀C₁C ₁₀C₂ +₁₀C₃ + . . . + ₁₀C₁₀

B 2¹⁰ - 1 D Both A and C.

4.How many ways are there to choose 3 men and 5 women from groups of 7 men and 8 women?

A 840 C 91

B 1411200 D 1960

5.Which is equivalent to _nC_r?

A _nC_r-2 + _nC_r-1C _n-1C_r + _n-1C_r+1

B _n-1C_r-1 + _n-1C_rD _nC_r-1 + _n-1C_r

6. The first three terms in the binomial expansion of (x + y)⁸ are

A x⁸, 8x⁷y, 28x⁶y²C x⁸, 8x⁸y, 28x⁸y²

B x⁸, x⁷y, x⁶y²D x⁸y, x⁷y, x⁶y

7. Which are the first three terms in diagonal 5 of Pascal's triangle?

A ₅C₀, ₅C₁, ₅C₂ C ₅C₅, ₅C₄, ₅C₃

B ₅C₁, ₆C₂, ₇C₃ D ₅C₅, ₆C₅, ₇C₅

8. Determine the number of paths from A to B, travelling only downward and to the right.

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