permutation

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 circular permutation With n = 6: (6 - 1)! 5! 5 x 4 x 3 x 2 x 1 = 120 ways

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 order of 9 starting players if only one pitcher is used at a time and the pitcher always bats last. (This means that 8 players are taken from the...

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 order of the arrangement each day for the next 41 years. (The same five paintings are okay as long as the hanging order is different.) What is the fewest...

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 seats. How many different permutations are there for these 12 friends? 12 taken 12 at a time is written as: 12P12 = 479,001,600

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 paintings taken 6 at a time is written as: 8P6 = 20,160

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 hooks. Who has more possible ways to hang his/her paintings? Jay's ways: 5 P 4 = 120 Nancy's ways: 5 P 5 = 120 Therefore, they have the same number of...

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 can the 1st and 2nd place be awarded?: We have a combinations problem of 10 choose 2. Using our permutations calculator, we see that: 10 P 2 = 90 ways

How many different ways could you arrange 5 books on a shelf? Using permutations, you can type in 5! and we get: 120 different ways.

A catering service offers 3 appetizers, 6 main courses, and 4 desserts. A customer is to select 2 appetizers, 3 main courses, and 3 desserts for a banquet. In how many ways can this be done? We use the combinations formula, and since each event is independent of the others, we multiply: 2...

Committees of 4 men 5 women form a group of 11 men and 11 women. We want combinations. 4 men from 11 men is the combination 11C4. Using our combinations calculator, we get: 11C4 = 330 5 women from 11 women is the combination 11C5. Using our combinations calculator, we get: 11C5 = 462 We...

A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 9 sophomores, 7 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen? We want combinations for freshmen, sophomores, juniors, and...

How many ways can 5 people be seated in 5 seats? We have the permutation 5!. Because the first seat can have 5 different people. The next seat has 5 - 1 = 4 people since one person is in the first seat The next seat can have 5 - 2 = 3 people since we have two people in the first two seats The...

Find the number of combinations and the number of permutations for 10 objects taken 6 at a time Combinations is written as 10 C 6. Using our combinations calculator, we get 210. Permutations is written as 10 P 6. Using our permutations calculator, we get 151,200.