a textbook search is considering 19 books for possible adoption. the committee has decided to select 5 of the 19 for furture consideration in how many way can id do so
Number of ways to select 5 of 19 is
C(19,5)
= 19!/(5!14!)
= 11628
most calculators have that function built-in
look for something like
nCr
A textbook search committee is considering
16
16 books for possible adoption. The committee has decided to select
4
4 of the
16
16 for further consideration. In how many ways can it do so?
To determine the number of ways to select 5 books out of 19 for future consideration, you can use the combination formula. The combination formula is given by:
C(n, r) = n! / (r!(n-r)!)
where n represents the total number of items and r represents the number of items to be chosen.
In this case, n = 19 (total number of books) and r = 5 (books to be chosen for future consideration). Plugging these values into the formula:
C(19, 5) = 19! / (5!(19-5)!)
Simplifying further:
C(19, 5) = 19! / (5! * 14!)
To calculate these factorials, we can use a calculator. Evaluating the equation, we get:
C(19, 5) ≈ 15,504
So, there are approximately 15,504 ways to select 5 books out of 19 for future consideration.
To find the number of ways to select 5 books out of 19 for future consideration, we can use the concept of combinations. The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of items
- r is the number of items to be selected
- ! denotes factorial, which means multiplying a number by all the positive integers less than it down to 1
In this case, n = 19 (total number of books) and r = 5 (number of books to be selected). Plugging those values into the formula, we can calculate the number of combinations:
C(19, 5) = 19! / (5!(19-5)!)
Simplifying the expression:
C(19, 5) = 19! / (5! * 14!)
Now, let's calculate the factorial terms:
19! = 19 * 18 * 17 * 16 * 15 * 14!
5! = 5 * 4 * 3 * 2 * 1
Substituting the values:
C(19, 5) = (19 * 18 * 17 * 16 * 15 * 14!) / (5 * 4 * 3 * 2 * 1 * 14!)
The 14! terms cancel out:
C(19, 5) = (19 * 18 * 17 * 16 * 15) / (5 * 4 * 3 * 2 * 1)
Evaluating the expression:
C(19, 5) = 116,280
Therefore, there are 116,280 ways to select 5 books out of a total of 19 for future consideration.