Number of subsets of length 7
126888
How can you show that $\binom {n}{7}=\sum_{k=7}^n \binom {k-1} {6}$?
91485
Finding an uncountable chain of subsets the integers
147484
For a set with N members, what is the number of set partitions in which each subset is either of size 1 or 2?
125040
Show by induction : $n^7-n$ is a multiple of 7
88595
Prob. 21, Sec. 17 in Munkres' TOPOLOGY, 2nd ed: Closure and complementation can result in at most 14 different sets
104527
Prove that there are two subsets of any cardinality-10 subsets of $\{1,2\dots,106\}$ that sum to the same number
47123
Suppose that a set has an odd number of elements. Explain why half of the subsets will have an odd number of elements
76405
Let n be an even integer. How many different ways can I choose subsets of the set {1,2...,n}
106397
Counting ways to partition a set into fixed number of subsets
139935
Show that any set of 7 distinct integers includes two integers $x$ and $y$, such that either $x-y$ or $x+y$ is divisible by 10
98850
A positional number system for enumerating fixed-size subsets?
44409
Number of Elements Not divisble by 3 or 5 or 7
107964
Simple combinatorics problem.
28453
Finding all partitions of a set
44214
The number of subsets of a set of cardinality $n$
113668
Uncountable chain of subsets of $\mathbb N$
139078
Infinite partition of $\mathbb N$ by infinite subsets