Important Formulas: Permutation and Combination | Quantitative for GMAT PDF Download

Permutation
The different arrangements of a given number of things by taking some or all at a time, are called permutations. This is denoted by ⁿP_r. Permutations are studied in almost every branch of mathematics, and in many other fields of science. In computer science, they are used for analyzing sorting algorithms.

Combination
Each of the different groups or selections which can be formed by taking some or all of a number of objects is called a combination. This is denoted by ⁿC_r.

Permutation and Combination Formulas

Number of all permutations of n things, taken r at a time, is given by

Number of all combinations of n things, taken r at a time, is given by

Important Points

• Factorial of any negative quantity is not valid.
• If a particular thing can be done in m ways and another thing can be done in n ways, then
  • Either one of the two can be done in m + n ways and
  • Both of them can be done in m × n ways
• 0! = 1
• 1! = 1
• If from the total set of n objects and ‘p1’ are of one kind and ‘p2’ and ‘p3’ and so on …. till pr are others respectively then
  

Permutation and Combination Formulas- Factorial

n ! = n(n-1)(n-2) …… 1 Eg. – 5! = 5(5-1)(5-2)(5-3)(5-4) = 5(4)(3)(2)(1)

Standard Truths

• 0! = 1
• n! only exists of n >= 0 and doesn’t exist for n < 0

Permutations Formulas

Number of ways in which Permutations out of n things r things can be SELECTED & ARRANGED (denoted by ⁿP_r ).

ⁿP_r = number of permutations (arrangements) of n things taken r at a time.

Formulas for Combinations

The number of ways in which r things at a time can be SELECTED from from n things is Combinations (represented by ⁿC_r).. ⁿC_r = Number of combinations (selections) of n things taken r at a time.

•  where n ≥ r (n is greater than or equal to r).