# How many subsets does 6 elements have?

If you have a set of 6 elements, you can make a total of 26 different subsets - including the empty set and the set itself.

### How many subsets can be made from a set with 6 elements?

If a set has six elements, for example {A, B, C, D, E, F}, then it may have the following subsets: - the set itself - 6 sets of five elements - 15 sets of four elements - 20 sets of three elements - 15 sets of two elements - 6 sets of one element - 1 set with no elements (the null set), for a total of 64 sets, which is 2^6, or 2…

### How many subsets with more than two elements does a set with 100 elements have?

To get the number of subsets of size less than 2: Total number of subsets of a set of size N is 2N Total number of subsets of size 1 is 100 Total number of subsets of size 0 is 1 Total number of subsets of size 2 is 100*99/2 = 4950 Sum up: 100 + 1 + 4950 = 5051 Subtract this from total subsets: 2100 - 5051 (Answer)

### We put n balls in p discernable boxes If balls are discernable Find combinations if a Every box can receive only 1 ball at most B Every box can receive any number of balls?

1) The amount of unique, single-element subsets of "A" is the amount of unique elements in "A". Your question states that we can also have no elements ("balls") in subsets. In Discrete Mathematics the amount of unique elements of the set "A" is often referred to as the "cardinality" of a set. This is denoted |A|. So the answer would be |A| + 1. (The ' + 1' accounts for the empty set) 2) If…

### Prove that A contains N elements and the different subsets of A is equal to 2?

Assuming the question is: Prove that a set A which contains n elements has 2n different subsets. Proof by induction on n: Base case (n = 0): If A contains no elements then the only subset of A is the empty set. So A has 1 = 20 different subsets. Induction step (n > 0): We assume the induction hypothesis for all n smaller than some arbitrary number k (k > 0) and show that…