different math subjects

i. In a combination, only selection is made. In a permutation, not only a selection is made, but also there is an arrangement of a definite order. ii. There is no order of selection in combinations. In permutation, order is a must. iii. Usually (i.e., except in special cases or trivial cases), the..

The fundamental principle of counting (F.P.C) states that if an operation can be performed in m different ways and if for each such choice, another operation can be performed in n different ways, then both operations, in succession can be performed in exactly mn diffe..

Arithmetic Progression (or simply A.P.) - Quantities are said to be in Arithmetic progression when they increase or decrease by a common difference..

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

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..

The number of permutations of n different things taken r at a time is the same as the number of ways of filling n letters and r blank spaces, supposed to be arranged in a straight line as shown above. Each blank is accommodating only one letter. We may fill the first blank with any one..

Question: Given five different green dyes, four different blue dyes and three different red dyes, how many combinations of dyes can be chosen taking atleast one green and one blue dye? Answer: The least number of dyes that a combination can have is 2. (one ..

Question: There are three different rings to be worn in 5 fingers with at most one in each finger. In how many ways can this be done? Answer: For the first ring, there are 4 options as one finger cannot have more than one ring. The remaining two fingers will have 3 and 2 optio..

Suppose two events E 1 and E 2 are to be performed in sequence, then if E 1 can be performed in 'm' ways and for each of these ways E 2 can be performed in 'n' ways, then the sequence E 1 E 2 can be performed in 'mn' different ways. This is known as the Fundamental Principle of..

The Greek letter S (read as sigma) denotes the sum. When written before the n t h term of series, implies, the sum of all terms obtained by giving to n the different values 1,2,3..