New posts in Combinations

All permutations of $1,2,...,n$ such that each element is larger than all previous elements or smaller than all previous elements

ways of selecting consecutive persons sitting at a table

Given three permutations of $\{1,2,\dots,n^3+1\}$, prove two of them have a common subsequence of length $n+1$.

The total number of subsets is $2^n$ for $n$ elements

Minimum distance between sequence a and all permutations of another sequence b

Rectangles in a $n \times n$ grid and the sum of the first $n$ cubes: a geometric connection?

Why my process is wrong:-How many ways are there to choose $5$ questions from three sets of $4$, with at least one from each set?

How many ways could the guests arrange themselves on a four person couch

Calculate lottery's second prize using combination - lottery probability question.

What's wrong in my solution? Ways of choosing 5 items from 3 catagory with 3, 6, 14 items, while having 1 item from each catagory.