Understanding Pascal's Triangle and Combinations

This lesson explains how to use Pascal's Triangle to evaluate combinations. It begins by showing how to form Pascal's Triangle using binomial coefficients and then introduces an alternative method of forming the triangle by starting with a row of ones and adding entries based on the sum of the two entries above. The lesson then demonstrates how to use Pascal's Triangle to evaluate combinations by locating specific entries in the triangle, with examples such as 7 choose 2, 9 choose 3, 12 choose 5, and 15 choose 6.

What is the first step in forming Pascal's Triangle using binomial coefficients?

• Use only even numbers

• Arrange numbers in a square

• Arrange binomial coefficients in a triangle

• Start with a row of zeros

In the initial rows of Pascal's Triangle, what pattern do the numbers follow?

• All numbers are zeros

• All numbers are twos

• All numbers are threes

• All numbers are ones

How is each new row formed in the alternative method of creating Pascal's Triangle?

• By dividing numbers from the previous row

• By multiplying numbers from the previous row

• By adding numbers from the previous row

• By subtracting numbers from the previous row

What is the sum of the numbers directly above a number in Pascal's Triangle?

• The number to its left

• The number itself

• The number to its right

• The number below it

How do you find the value of a combination using Pascal's Triangle?

• Locate the entry in the diagonal

• Locate the entry in the first column

• Locate the entry in the last row

• Locate the entry in the specified row and column

What is the value of 7 choose 2 using Pascal's Triangle?

• 15

• 21

• 28

• 35

Which row and column in Pascal's Triangle would you look at to find 9 choose 3?

• Row 7, Column 2

• Row 10, Column 4

• Row 9, Column 3

• Row 8, Column 2

What is the value of 12 choose 5 in Pascal's Triangle?

• 792

• 1152

• 924

• 1024

To find 15 choose 6, which row and column should you refer to in Pascal's Triangle?

• Row 14, Column 5

• Row 13, Column 4

• Row 16, Column 7

• Row 15, Column 6

What is the value of 15 choose 6 using Pascal's Triangle?

• 55

• 35

• 75

• 95