factorial

How many possible batting orders are there for a baseball team with 9 players? 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880 batting orders

Sara wants to arrange the seven scrabble letters she has in every possible way so she can determine if she has a 7-letter word. how many different ways are there for Sara to arrange all seven letters? 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040 ways

A soccer team has picked its five best players to take part in penalty kicks to determine the winner of a soccer match that is tied. Each of the five players will get one shot against the opposing team's goalie. The coach needs to decide the order in which the five players will take their shots...

Abbey knew that the combination for her locker had the numbers 36, 12, 8, and 40, but she couldn't remember the right order of the numbers. How many different possibilities are there for the lock combination using the four numbers? First number could be 4 choices, then 3, then 2, then 1. So we...

Laura has three errands to complete. She must wash the dishes, mow the lawn, and paint a fence. How many ways can Laura arrange the order of the three errands? 3! = 3 * 2 * 1 = 6 ways

Find r in P(7, r) Recall the permutations formula: 7! / (7-r!) = 840. We run 7! through our search engine and we get: 7! = 5040 5040 / (7 - r)! = 840 Cross multiply, and we get: 5040/840 = 7 - r! 6 = (7 - r)! Since 6 = 3*2*! = 3!, we have; 3! = (7 - r)! 3 = 7 - r To solve for r, we type...

A tourist in Ireland wants to visit six different cities. How many different routes are possible? We want 6! which is 720

The coach writes the batting order on a piece of paper. How many different ways could the list be written? We have 9 people in a line up. The total lineups are shown by: 9 * 8 * 7 * ... * 2 * 1 Or, 9!. Typing 9! in our search engine and we get 362,880

Make 19 using only four four's 4!-4-4/4 To prove our work, we have: 4! = 24 24 - 4 = 20 Since 4/4 = 1, we have: 20 - 1 = 19

From 9 names on a ballot, a committee of 4 will be elected to attend a political national convention. How many different committees are possible? A. 3024 B. 15,120 C. 1512 D. 126 We want unique combinations, so we have 9 choose 4, or 9C4. Typing this into the search engine, we get: 9C4 = 126...

Write in set builder form {all possible numbers formed by any two of the digits 1 2 5} With 3 numbers, we got 3! = 6 possible numbers formed by the two digits 12 15 21 25 51 52 In set builder notation, we write this as: {x : x ∈ {12, 15, 21, 25, 51, 52}) x such that x is a element of the set...

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: n! = n · (n - 1) * (n - 2) * ... * 3 * 2 * 1 Written in partially expanded form, n! is: n! = n * (n - 1)! Substitute n = 1 into this...

A mother duck lines her 13 ducklings up behind her. In how many ways can the ducklings line up? In position one, we can have any of the 13 ducks. In position two, we can have 12 ducks, since one has to occupy position one. We subtract 1 each time until we fill up all 13 positions. We have: 13...

If there are 8 girls entered in a race, how many different ways can the runners place first, second, and third? We want 8 choose 3, or 8C3. Type 8C3 into the search engine, and we get 56 different ways to place first, second, and third.

A restaurant offers a special pizza with any 5 toppings. If the restaurant has 17 topping from which to choose, how many different special pizzas are possible? We have 17 choose 5, or 17C5. Type this into the search engine, and we get 6,188 different special pizzas available.

You and 5 friends go to a concert. how many different ways can you sit in the assigned seats? With 6 possible seats, the number of unique arrangements is: 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Tony has 6 cds that he is giving away. He lets his best friend choose 3 of the 6 cds. How many groups of 3 cds are possible? This problem asks for unique combinations. We want 6 choose 3, or 6C3. Go to the search engine, and type in 6C3, we get 20 possible groups.

The doubling time of a population of flies is 8 hours. a) By what factor does a population increase in 24 hours? b) By what factor does the population increase in 2 weeks? a) If the population doubles every 8 hours, then it doubles 3 times in 24 hours, since 24/8 = 3. So 2 * 3 = 6. The...

Serial numbers for a product are to made using 4 letters followed by 4 numbers. If the letters are to be taken from the first 5 letters of the alphabet with repeats possible and the numbers are taken from the digits 0 through 9 with no repeats, how many serial numbers can be generated? First 5...