Permutations
By: Arush Gupta
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The concept of permutations, their history, and provides examples with calculations. Permutations are arrangements or listings of objects where the order is important. The formula for calculating permutations is presented, along with examples of how to apply it to different situations.
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2018/2019
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Permutations
By: Arush Gupta
What is a Permutation?
A permutation is an arrangement, or listing, of objects in which the order is important.
Permutation is used when we are counting without replacement and the order matters.
nPr
The formula to solve
permutations is P(n,r)= n!
where,
n is the total number of
objects in the set
P is the number of
permutations, and
r is the number of choosing
objects from the set.
Factorial
In math the explanation mark
means factorial.
An example is 3! = 3x2x1=
Also the value of 0! is 1
5!= 5 x 4 x 3 x 2 x 1=
6!= 6 x 5 x 4 x 3 x 2 x 1=
Trivia Time!!!
- What is the answer for 5 factorial?
- True or False: the order matters in permutations.
- How many different ways can you group A, B, C, and D- SHOW ALL WORK!
- What is the answer for 8 factorial?
- True or False: there are 3 ways to put a, b, c- explain your reasoning/show your work
- If you have person A, B, C, D, E, and F, and you have seat 1, 2, 3, and 4, how many ways can the people sit in the seats?
- Jacob has 5 shirts, 6 pants, and 4 jackets. In how many ways can he select 1 shirt, 1 pant, and 1 jacket? SHOW ALL WORK!!!
- The courthouse flies the city, state and country flags. How many ways can the flags be arranged on the flag time?
Trivia Time!!!
- 10 students have entered in a contest in
which the top 3 will get a prize. How many
possible ways are there to get the prize
winners? SHOW ALL WORK!!!
- 4 cheerleaders are having their pictures
taken for the school annual. How many
different ways can they be arranged?
- You have 5 reindeer, Dancer, Prancer, Comet, Dasher, and Rudolph. You want to have 3 fly your sleigh. How many different ways can you arrange the reindeer?
- How many different ways are there to arrange the letters CAT?
- How many different ways are there to arrange the letters DANCE?
- True or False: there are 30 different ways to arrange the letters HAND. Explain your reasoning.
- True or False: there are 3 different ways to arrange the letters Y, and Z.