Practicing Entrance Exams

Binomial Theorem

In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion. According to the theorem, it is possible to expand the power (x + y)ⁿ into a sum involving terms of the form ax^by^c, where the exponents b and c are non negative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

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Permutations and Combinations

Factorial Notation:
Let n be a positive integer. Then, factorial n, denoted n! is defined as:

n! = n(n - 1)(n - 2) ... 3.2.1.

We define 0! = 1.
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6
4! = 4 x 3 x 2 x 1 = 24.
5! = 5 x 4 x 3 x 2 x 1 = 120.

Permutations: 

The different arrangements of a given number of things by taking some or all at a time, are called permutations.

All permutations (or arrangements) made with the letters a, b, c by taking two at a time are (ab, ba, ac, ca, bc, cb).

All permutations made with the letters a, b, c taking all at a time are:
( abc, acb, bac, bca, cab, cba)

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