Pascal's Triangle, Comb., Perm., etc.

Factorials and Pascal's Triangle

100

Without using a calculator, what is 4!

24

200

Evaluate 6!/3!

6!/3! = 120

300

Using the triangle, find ₇C₃

35

400

What is the coefficient for the term x^7 y^2 in the expansion of (x + y)^9 ?

36

500

Using the triangle, find ₅C₄

5

Binomial Theorem and Expansion

100

Using the shortcut for (x+y)⁴, what is the 3rd term in the answer?

6x²y²

200

Expand (x-y)⁵

1x⁵  - 5x⁴y+ 10x³ y² - 10x² y³ + 5xy⁴ - 1y⁵

300

Using the shortcut, what is the 6th term of (x+2)⁶ ?

192x

400

Fastest team wins....

Draw Pascal's triangle up to and including the line

1   4  .....

Teacher will check answers.

500

Using the shortcut for (x+3)³, what is the 2nd term in the answer?

9x²

Permutations

100

Set up but do not evaluate: In how many different ways can 9 floats line up for a parade?

9! or 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

200

A customer can choose one of 4 different salad mixes, one of 8 different toppings, and one of 5 dressings. How many different salads can she create?

8 x 4 x 5 or 160 different salads

300

 In how many different ways can you answer a 14 question true or false quiz?

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 or 2^14

16384

400

READ CAREFULLY...

In a certain state, the license plate is made up of 3 letters followed by 4 numbers.

 If the letters may not be used more than once, and the first number must be greater than 5, but with the last 3 numbers,  the numbers can be reused, how many different license plates are possible?

26 x 25 x 24 x 4 x 10 x 10 x 10

62,400,000

500

A group of 25 people are completing in an essay competition.  The top 5 winners each win a monetary prize of $500, $400, $300, $200, or $100 based on what place they come in.  Find the number of possibilities in this scenario.

6,375,600

Combinations and Permutations

100

Use the P or C formulas:

Find ₇P₂

42

200

Using the P formula, find:

₁₂P₆

665,280

300

Using the C formula, find ₁₁C₄

330

400

Use the C formula:

₁₀C₄

210

500

 A box contains 12 black and 8 green marbles.

 In how many different ways can you choose 3 black marbles and 2 green marbles?

(It's a 2 part problem)

220 x 28=

6160

Cool Triangle Tricks

100

Think of the cool tricks of the triangle.

Using the triangle only, NO CALCULATORS,  what is 11³ ?

1,331

200

What is Pascal's first name?

Blaise

300

Using the triangle SOCK TRICK, NO CALCULATOR, what is the sum of 

1  3  6  10  15  21

56

400

True or False:  You can do Permutation problems using the triangle only.

False (only combination problems)

500

Using the triangle only (no calculator), what is 11⁷?

     19,487,171