Facts of Life
What is 0!
1
20 politicians are running for the offices of president, secretary and treasurer. In how many ways can these offices be filled?
6840
What is a way of arranging things in an ordered fashion where order matters
Permutation
You've decided to have a Disney marathon over the weekend. The movies you plan on watching are The Lion King, Aladdin, Beauty and the Beast, The Little Mermaid, Mulan, Pocahontas, and Hercules. Thanks to your POW, you know you want to start with Pocahontas. How many different viewing orders can there be?
720
If there are 25 clips in a bag: 5 are red, 4 are blue, 10 are green, and 6 are yellow. What is the probability that you will select a green clip from the bag? Express your answer as a percent
40%
Alan and Mike want to attend 10 major league games at different parks this year. They are trying to decide in which order to visit the parks. In how many different orders can they visit the 10 different parks if they visit each once?
3,628,800
How many ways can you re-arrange 2 letters in the alphabet.
650
What is a way of arranging objects things where order does not matter.
You've decided to start a band! For your band, you want a lead singer, a drummer, 2 backup singers (one for slow songs and one for uptempo), a guitarist, and a keyboard player. You want to be the lead singer, but you held auditions for the other roles. Two people have auditioned to be the drummer, 8 people have auditioned to be a backup singer, 2 people have auditioned to be the guitarist, 4 people have auditioned to be a keyboard player. How many different bands could you form.
896
Three coins will be tossed in the air. How many different outcomes of heads and tails are there?
8
How many ways can 7 people be arranged around a circular table?
5040
We need 10 people to make a Dance Committee. There are 11 boys and 8 girls. How many ways can I make this committee?
What is the permutation formula and symbol?
nPr
n!/(n-r)!
How many ways can you pick a team of 4 people from a group of 6 men and 7 women, when there must be 2 of each gender
315
Verizon offers 6 phones, 12 texting plans, 4 calling plans, and 3 data plans. How many different plans can you make if you choose 1 phone, 1 calling plan, 1 data plan, and one texting plan?
864
What factorial is equal to 120
5
There are 10 contestants in the state quiz bowl competition. The top two contestants will go on to compete at the national quiz bowl competition. How many different match ups can there be at the national quiz bowl competition? How may different ways can first and second place be chosen?
45
90
What is the combination formula and symbol?
nCr
n!/r!(n-r)!
You are to choose the members of your group from 10 girls and 8 boys. If you want to have 3 girls and 3 boys to form your group, how many ways can you choose?
6720
What is the probability of rolling 2 die and getting a sum of seven. Express your answer as a simplified fraction?
1/6
A set of encyclopedia is arranged on a shelf. The set has 12 books. How many incorrect arrangements are possible?
479001599
There are 56 ways to make a pizza. There are 8 toppings to choose from. How many toppings can you put on the pizza?
3
What does n and r stand for?
n=the total number of items
r=the number of items we are choosing.
Ms. Bagwell has a lock with a four digit combination. She does not like the numbers 6,0, or 1 and will not use them in her combination. How many different 4 digit combinations can she choose from if her combination must be an even number and must start with 7.
147
How many “words” with five letters exist that start with a vowel and end with an S? Note: They don’t have to be real words. Vowels are A, E, I, O, and U.
87,880