How to simplify this combinatorial formula and solve the cardinality of the intersection?
111954
Computing the cardinality of a combinatorial set
60860
Combinatorial proof of $\sum_{i = 0}^{n} \binom{i}{r - 1} = \binom{n + 1}{r}$ and then use result to find a formula for $1^2 + 2^2 + \ldots + n^2$
17580
Combinatorics That Looks Similar to Vandermonde's Identity
74294
How to simplify $\sum_{i=1}^{k}\binom{n + i - 1}{i}$?
152342
$x_1+x_2+\cdots+x_n\leq M$: Cardinality of Solution Set is $C(M+n, n)$
8458
Combinatorics problem based on Ferrers graph
26919
Intersection of Connected Sets
156383
Proving a combinatorial identity without double counting
24045
Efficiently compute Intersection of two Sets in Java?
5215
Can the principle of inclusion/exclusion be used to count elements in the intersection of a sequence of sets?
70327
the numer of partial function between two sets in combinatoric way
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
143573
Problem (1.8) A Path to Combinatorics Solution Verification.
142978
combinatorics: sum of product of integer compositions
44484
Combinatorial identity $i{n \choose i } =n {n-1 \choose i - 1}$
109764
Find the cardinality of the quotient of $\mathbb R$ in respect to R
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$