A student is given a reading list of ten books from which he must select four for an outside reading requirement. In how many ways can he make his selections?
You need to ask yourself...
Does order matter? If it did this would be a permutation question.
In this case order does not matter, so it is a combination question
10Choose4
To find the number of ways the student can make his selections, we need to use the concept of combinations.
The number of ways to select 4 books out of a list of 10 is calculated using the combination formula, which is:
nCr = n! / (r!(n-r)!)
Where n is the total number of books and r is the number of books to be selected.
In this case, we have n = 10 and r = 4.
Therefore, the number of ways the student can make his selections is:
10C4 = 10! / (4!(10-4)!) = 10! / (4!6!) = (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1) = 210
So, the student can make his selections in 210 different ways.
To calculate the number of ways the student can make his selections, we need to use the concept of combinations.
The number of combinations, denoted as C(n, r), represents the number of ways to choose r items from a set of n items without considering their order.
In this case, the student needs to select 4 books from a reading list of 10 books. Therefore, the number of ways the student can make his selections can be calculated using the combination formula:
C(10, 4) = 10! / (4! * (10-4)!)
Here's how the calculation works step by step:
1. Calculate the factorial of 10: 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800.
2. Calculate the factorial of 4: 4! = 4 * 3 * 2 * 1 = 24.
3. Calculate the factorial of (10-4): (10-4)! = 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720.
4. Divide the result of step 1 by the product of step 2 and step 3:
10! / (4! * (10-4)!) = 3,628,800 / (24 * 720) = 210.
Therefore, the student can make his selections in 210 different ways.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
1, 2, 3, 4.
2, 3, 4, 5.
3, 4. 5, 6.
4, 5, 6, 7.
5, 6, 7, 8.
6, 7, 8, 9.
7, 8, 9, 10.
8, 9, 10, 1.
9, 10, 1, 2.
10, 1, 2, 3.
There are 10 different ways.