permutations

A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential. If one wants to pur...

Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix all these elements in all possible orders. They also decide...

Consider a permutation sampled uniformly at random from the set of all permutations of {1, 2, 3, ..., n} for some n ≥ 4. Let X be the event that 1 occurs before 2 in the permutatio...

When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers (i.e., 1, 2, 3, 4, 5, and 6) is

Consider a permutation sampled uniformly at random from the set of all permutations of {1, 2, 3, ..., n } for some n ≥ 4. Let X be the event that 1 occurs before 2 in the permutati...

Two wizards try to create a spell using all the four elements, water, air, fire, and earth . For this, they decide to mix all these elements in all possible orders. They also decid...

Let $$U = \{ 1,2,....,n\} $$, where n is a large positive integer greater than 1000. Let k be a positive integer less than n. Let A, B be subsets of U with $$|A| = |B| = k$$ and $$...

Let $$G$$ be a graph with $$100!$$ vertices, with each vertex labelled by a distinct permutation of the numbers $$1,2, … , 100.$$ There is an edge between vertices $$u$$ and $$v$$...

Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes...

Suppose we uniformly and randomly select a permutation from the 20! permutations of 1, 2, 3,..., 20. What is the promutations that 2 appears at an earlier position than any other e...

Given a set of elements N = {1, 2, ....., n} and two arbitrary subsets $$A\, \subseteq \,N\,$$ and $$B\, \subseteq \,N\,$$, how many of the n! permutations $$\pi $$ from N to N sat...

A bag contains 10 blue marbles, 20 green marbles and 30 red marbles. A marble is drawn from the bag, its colour recorded and it is put back in the bag. This process is repeated 3 t...

A program attempts to generate as many permutation as possible of the string “abcd” by pushing the character a,b,c,d in the same order onto a stack, but it may pop off the top char...