# Math

posted by .

Assume that the set S has 10 elements.

How many subsets of S have at most 4 elements?

This question is from the section in my book called "Counting Partitions: Combinations." I would greatly appreciate any help! Thanks!

• Math -

It seems to me there are 10 ways to pick subsets of 1 element; 10!/(8! 2!)= 45 subsets with 2 elements; 10!/(7!3!) = 120 with three elements and 10!/(6!4!) = 210 subsets with four elements
The total is 385.

• Math -

Hey, thanks! However, that answer was not right. Any other ideas? You seem to be on the right track... This problem really confuses me.

• Math -

Ok, the answer is 386! Yay! However, I am not sure why the answer is not 385.... maybe because we had to add c(10,0) into the mix. Thanks so much for the help... I wouldn't have gotten the answer had it not been for your help!

## Similar Questions

1. ### Data Management

List all permutations of the elements of the set {+, -, *) List all subsets (combinations) of the elements of the set {+, -, *)
2. ### Math

How many subsets of a set with 100 elements have more than one element?
3. ### Combinations

Assume that the set S has 10 elements. How many subsets of S have at most 4 elements?
4. ### math

Assume that the set S has 14 elements. How many subsets of S have at most 4 elements?
5. ### math

For the set X={m,n.p,q,r,s}, let R be the relation on P(X) (power set) given by A R B iff A and B have the same number of elements. List all the elements in {m}/R (equivalence class); in {m,n,p,q,r,s}/R. How many elements are in X/R?
6. ### Finite MAth

Assume that the set S has 7 elements. How many subsets of S have at most 3 elements
7. ### Math(combinations) Help

Let Pn be the set of all subsets of the set [n]={1,2,…,n}. If two elements of P5 are chosen at random, the expected number of elements (of [n]) that they have in common can be expressed as a/b where a and b are coprime positive integers. …
8. ### math

Let Pn be the set of all subsets of the set [n]={1,2,…,n}. If two distinct elements of P5 are chosen at random, the expected number of elements (of [n]) that they have in common can be expressed as a/b where a and b are coprime positive …
9. ### Math

Let n be any counting number. Using the two questions above as a guide, how many subsets does the set {1,2,3,...,n−1,n} have?
10. ### Set Theory

Let the Universal Set, S, have 136 elements. A and B are subsets of S. Set A contains 34 elements and Set B contains 98 elements. If Sets A and B have 22 elements in common, how many elements are in A but not in B?

More Similar Questions