How many ways can you get a bunch of 4 books to give a friend if you have 30 books (15 novels, 10 history book and 5 math books)?
Without any constraints, you have 30 to choose from for the first, 29 for the second, 28 for the third, and 27 for the fourth.
But there are 4! ways to choose the same 4 books, so using the multiplication principle, the number of ways to find 4 books is
30*29*28*27/4!
=30!/(4!(30-4)!)
=C(30,4)
The last line is a "function" called combination, or n choose r, where we choose r objects from n, and order of choice is not important.
To find the number of ways to choose a bunch of 4 books out of the given collection of 30 books (15 novels, 10 history books, and 5 math books), we can use the concept of combinations.
First, we need to figure out the number of ways to select the 4 books from each category and then multiply those numbers together to get the total number of combinations.
For the novels:
We need to choose 4 books from 15. The formula for combinations is nCr, which represents the number of combinations of selecting r items from a set of n items. In this case, it is 15C4, which can be calculated as follows:
15C4 = 15! / (4! * (15-4)!) = 15! / (4! * 11!)
Similarly, we can calculate the number of combinations for the history books and the math books:
10C4 and 5C4 respectively.
Finally, to get the total number of combinations, we multiply the three results together:
Total combinations = (15! / (4! * 11!)) * (10! / (4! * 6!)) * (5! / (4! * 1!))
Calculating these values will give us the number of ways to select a bunch of 4 books from the given collection.