Combinatorics chapter 6

Combinations

100

Compute the following C(7,3)

What is 35?

200

There are 25 students in Miss Johnston's class. In how many ways can she select 4 students to work in the tangrams center?

What is 12650 or 25*23*22?

300

A 4-card poker hand is dealt at random from a standard 52-card deck. What is the total number of possible hands if the hand contains 2 5's and 2 7's?

What is 36?

Permutations

100

Evaluate: P (5,3)

What is 60?

200

Evaluate: P (10,7) * P (13,4)

What is 604800 * 17160 or 10378368000?

300

A teacher is making a multiple choice quiz. She wants to give each student the same questions, but have each student's questions appear in a different order. If there are twenty-seven students in the class, what is the least number of questions the quiz must contain?

What is 5*4*3*2*1 or 120?

Multiplication Principle

100

Peggy's Princess shop sells young girl's baby dolls. There are 2 different characters that have 6 accessories sold separately. In how many ways can the dolls and their accessories be sold?

What is 12 or 2*6?

200

Barbara wants to get her son, John's, outfits ready for the week. She has 12 shirts to choose from, along with 4 pairs of shorts and 3 pairs of shoes. How many outfits can she make for John?

What is 144 or 12*4*3?

300

California's government issues license plates that include 3 numbers, followed by 2 letters, and ending with another 3 numbers. IMPORTANT: Repetition is not allowed. How many license plates can be made?

What is 98280000 or 10*9*8*26*25*7*6*5?

~WILD CARD ~

100

What is the first number of the 12th row in Pascal's Triangle?

What is 1?

200

These are ordered arrangements of a set of distinct elements.

What is a permutation?

300

Evaluate: 1. P (n,2) 2. P (n,n-1)

What is 1. n * (n-1) 2. n!