different types of patterns in mathematics

Question: A committee of 6 is chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done, if two particular women refuse to serve on the same committee? Answer: Let the two ladies who refuse to work on the same comm..

Row Matrix - A matrix having only one row is called a row-matrix. For example: A[1 3 2 -2] is a row matrix of order 1 x..

Quantities are said to be in Arithmetic progression when they increase or decrease by a common difference..

The number of circular permutations of n different objects is (n-1)..

We have seen the application of matrices and determinants in solving system of linear equation with three unknown variables. Matrices and determinants are also widely used in solving large system of linear equation. Some of these methods are Gauss-elimination method, Gauss-Jordan method etc. They a..

There are 8 cars plying between two towns A and B. In how many ways can a person go from one town to the other and return by a different ca..

In how many different arrangements can 6 gentlemen and 6 ladies sit around a table if i) there is no restriction and ii) no two ladies sit side by sid..

Permutations - The different arrangements that can be made with a given number of things taking some or all of them at a time are called permutations. The symbol n P r or P(n,r) is used to denote the number of permutations of n things taken r at a tim..

Question: Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many different ways can we place the balls so that no box remains empty? Answer: Given 5 balls can be placed in 3 boxes as..

C(n,r) is the required combination by definition. Each of these combinations consists of a group of r dissimilar things, which can be arranged among themselves in P(r,r) = r! ways. But the number of permutations of n different things taken r at a time is P(n,r)..