Beth’s mother told her that she can choose four books from the book fair. There are six books now Beth would like to have. How many different combinations of four books could Beth choose from those six?
To solve this problem, we can use the combination formula:
nCr = n! / r!(n-r)!
where n is the total number of items, r is the number of items to choose, and ! denotes factorial (the product of all positive integers up to that number).
In this case, n = 6 (the total number of books available) and r = 4 (the number of books Beth can choose). Using the formula:
6C4 = 6! / 4!(6-4)!
6C4 = 6! / 4!2!
6C4 = (6 x 5 x 4 x 3) / (4 x 3 x 2 x 2)
6C4 = 15
Therefore, there are 15 different combinations of four books that Beth could choose from those six.
To find the number of different combinations of four books that Beth can choose from the six available, we can use the concept of combinations.
The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
Where:
n = total number of items
r = number of items to be selected
! = factorial
In this case, Beth wants to choose 4 books from the 6 available. So, n = 6 and r = 4.
Plugging these values into the formula, we get:
C(6, 4) = 6! / (4!(6-4)!)
= 6! / (4!2!)
= (6 * 5 * 4 * 3 * 2 * 1) / [(4 * 3 * 2 * 1) * (2 * 1)]
= (720) / (48)
= 15
Therefore, there are 15 different combinations of four books that Beth can choose from the six available.
To solve this problem, we can use the concept of combinations, specifically the combination formula. The combination formula is given by:
C(n, r) = n! / (r! * (n - r)!)
where C(n, r) represents the number of combinations of choosing r items from a set of n items.
In this case, Beth has 6 books to choose from and she needs to choose 4 books. So, n = 6 and r = 4.
We can plug these values into the combination formula to calculate the result:
C(6, 4) = 6! / (4! * (6 - 4)!)
= 6! / (4! * 2!)
= (6 * 5 * 4 * 3 * 2 * 1) / ((4 * 3 * 2 * 1) * (2 * 1))
= 15
Therefore, there are 15 different combinations of four books that Beth can choose from the six available books.