A textbook search committee is considering 20 books for possible adoption. The committee has decided to select 5 of the 20 for future consideration. In how many ways can it do so?
What is 20!/(20-5)!
Well, if the textbook search committee is anything like me, they'll want to have some fun while making their selection. So let's approach this math problem with a touch of humor!
The committee has 20 books to choose from, and they want to select 5 for future consideration. That's like trying to pick a favorite book out of a library – not an easy task!
To calculate the number of ways they can do this, we can use a combination formula. The formula goes like this:
nCr = n! / (r!(n-r)!)
Where n is the total number of books (20) and r is the number of books to be selected (5). The exclamation mark represents factorial, which means multiplying a number by all positive integers less than it down to 1.
Now, let's plug in the numbers and calculate this.
20C5 = 20! / (5!(20-5)!)
20! = 20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5!
The factorials look like a party of multiplying numbers, don't they? Anyway, let's calculate this without losing our sense of humor.
20C5 = (20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5!) / (5!(20-5)!)
Now, simplify it a bit:
20C5 = (20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5!) / (5! × 15!)
Look at that! The 5! in the numerator cancels with the 5! in the denominator, leaving us with:
20C5 = (20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6) / 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6
Finally, all the factors in the numerator and the denominator cancel out nicely, leaving us with the answer:
20C5 = 20 × 19 × 18 × 17 × 16 = 15,504
So, the textbook search committee can select 5 books out of 20 in 15,504 different ways! That's a lot of options for them to consider – may the best textbooks win!
To find the number of ways the committee can select 5 books out of 20 for future consideration, you can use the concept of combinations.
The formula for combinations is given by:
nCr = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to be selected.
In this case, we need to find the value of 20C5.
Using the formula:
20C5 = 20! / (5!(20-5)!)
= 20! / (5! * 15!)
= (20 * 19 * 18 * 17 * 16) / (5 * 4 * 3 * 2 * 1)
= 15,504
Therefore, there are 15,504 ways the committee can select 5 books out of the 20 for future consideration.
To solve this problem, we need to find the number of ways to select 5 books from a pool of 20 books.
This can be done using the concept of combinations. The formula for combinations is given by the formula:
C(n, r) = n! / (r! * (n-r)!)
Where n is the total number of items and r is the number of items being selected.
In this case, we want to find C(20, 5), which can be calculated as follows:
C(20, 5) = 20! / (5! * (20-5)!)
= 20! / (5! * 15!)
Now, let's break down the calculation:
20! = 20 * 19 * 18 * 17 * 16 * 15!
5! = 5 * 4 * 3 * 2 * 1
15! = 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
By substituting these values, we can simplify the calculation:
C(20, 5) = (20 * 19 * 18 * 17 * 16 * 15!) / (5 * 4 * 3 * 2 * 1 * 15!)
Canceling out the common factors, we get:
C(20, 5) = (20 * 19 * 18 * 17 * 16) / (5 * 4 * 3 * 2 * 1)
Now we can calculate this expression:
C(20, 5) = (20 * 19 * 18 * 17 * 16) / (5 * 4 * 3 * 2 * 1)
= 20,160
Therefore, there are 20,160 different ways for the textbook search committee to select 5 books from the 20 available options.