combinations

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...

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 $$...

There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same colour is

Suppose that everyone in a group of N people wants to communicate secretly with the N - 1 others using symmetric key cryptographic system. The communication between any two persons...

Four fair six-sided dice are rolled. The probability that the sum of the results being 22 is X/1296. The value of X is__________

The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the comp...

Let $$G$$ be a complete undirected graph on $$6$$ vertices. If vertices of $$G$$ $$\,\,\,\,$$ are labeled, then the number of distinct cycles of length $$4$$ in $$G$$ is equal to

The following function computes the value of m C n correctly for all legal values m and n (m≥1,n≥0 and m>n) int func(int m, int n) { if (E) return 1; else return(func(m -1, n) + fu...

Mala has a colouring book in which each English letter is drawn two times. She wants to paint each of these 52 prints with one of $$k$$ colours, such that the colour-pairs used to...

$$n$$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of...

Let $$A$$ be a sequence of $$8$$ distinct integers sorted in ascending order. How many distinct pairs of sequence, $$B$$ and $$C$$ are there such that i) Each is sorted in ascendin...

A multiset is an unordered collection of elements where elements may repeat ay number of times. The size of a multiset is the number of elements in it counting repetitions. (a) wha...

The number of binary strings of $$n$$ zeros and $$k$$ ones such that no two ones are adjacent is: