Need help with these-

1.How many groups of 4 fabrics can be selected from 7 fabrics?

2.The school photographer wants to photograph 3 students from a club with 14 members. How many combinations can be made?

3.Philip wishes to check 2 books out of his school library. If the library contains 800 books, in how many ways might Philip make his choice of books?

Thanks
-MC

C(n,k) = n!/[ (n-k)!k! ]

for example if n = 7 and k = 4
C(7,4) = 7! /[ 3! 4! ]
= 7*6*5 *4! /[3*2*1 *4!]
4! cancels top and bottom
6 cancels top and bottom
= 7*5
=35

Now try n = 14, k = 3
and n = 800, k = 2

Nevermind I got all the answers:

1. 35 groups
2. 364 combinations
3. 319,600 choices

-MC

..Oops just saw that Damon. Thanks!

-MC

1. To find out how many groups of 4 fabrics can be selected from 7 fabrics, you can use the combination formula. The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items you want to select.

In this case, n = 7 (the total number of fabrics) and r = 4 (the number of fabrics we want to select).

Using the formula, you can calculate:
C(7, 4) = 7! / (4!(7-4)!) = (7*6*5*4!) / (4!(3!) = 7*6*5 / (3*2*1) = 35

So, there are 35 groups of 4 fabrics that can be selected from the 7 fabrics.

2. For the second question, you want to know how many combinations can be made when selecting 3 students from a club with 14 members. Again, we can use the combination formula.

Here, n = 14 (total number of club members) and r = 3 (number of students we want to select).

Using the formula, we have:
C(14, 3) = 14! / (3!(14-3)!) = (14*13*12!) / (3!(11!)) = 14*13 / (3*2*1) = 364

So, there are 364 different combinations of 3 students that can be made from the club with 14 members.

3. In the third question, Philip wants to check out 2 books from a library that contains 800 books. To determine the number of ways Philip can make his choice, we can use the combination formula once again.

Here, n = 800 (total number of books in the library) and r = 2 (number of books Philip wants to choose).

Using the combination formula, we get:
C(800, 2) = 800! / (2!(800-2)!) = (800*799*798!) / (2!(798!)) = 800*799 / (2*1) = 319,600

So, Philip has 319,600 different ways to choose 2 books from a library of 800 books.