Prove 0! = 1 Let n be a whole number, where n! represents: The product of n and all integers below it through 1. The factorial formula for n is...
The tip off for this problem is the 2 phrases: circular table arranged Whenever you see these 2 phrases together, the problem is asking for a...
The formula is nC2 - rC2 + 1 In this problem: n = 8 and r = 3 8C2 = 28 3C2 = 3 Evaluating, we have: 28 - 3 + 1 26 [MEDIA]
Use our letter arrangement calculator: [MEDIA]
This is a symbol for a triple factorial. We have n!!! = n * (n - 3) * (n - 6) * ... * 1 Our subtraction of 3 never goes below one. 12!!! = 12 *...
10!= 10 x 9 x 8 x 7 x 6! So we have: 10 x 9 x 8 x 7 x 6!/6! 6! cancels, so we have: 10 x 9 x 8 x 7 5040 [MEDIA]
Evaluate 6!/3!5! 6!= 6 * 5! 6 * 5!/3!5! 5!'s cancel 6/3! 3! = 6, so we have: 6/6 = 1 [MEDIA]
How many ways are there to hang 5 paintings on 5 hooks? 5! = 5 x 4 x 3 x 2 x 1 5! = 120
A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many different ways are there to arrange the batting...
An eccentric millionaire has 5 golden hooks from which to hang her expensive artwork. She wants to have enough paintings so she can change the...
One thousand people in. room decide to shake hands with every other person in the room. Instead of one handshake per couple, each person must...
If 100 people are required to introduce themselves to each other and shake hands with each person one time, how many handshakes will take place?...
Five players are going to be picked to start a basketball game. If there are 13 players on the team, how many different combinations of 5 starting...
Eight people have volunteered for a secret mission that requires only 3 people. How many different combinations are possible? We want 8...
A music camp with 50 students decided to break the students into barbershop quartets to see which combination of four students sounded the best....
Twelve friends went to a movie theater. Because the movie was boring, they decided to figure out how many different ways they could sit in the 12...
Mrs. Lopez gave a homework assignment over summer vacation to read three books from the following list: a) Call of the Wild b) Wuthering Heights...
A mathematician has 8 favorite paintings and only 6 wall hooks to hang the paintings. How many different ways can she hang the paintings? 8...
Jay has 5 paintings that he plans to display on a wall that only has 4 books. Nancy has 5 paintings that she plans to display on a wall with 5...
Ten people are competing for the title of "Best Singer in the World". There will be a 1st place and a 2nd place awarded. How many different ways...
Separate names with a comma.