BodhiAI

Nov. 15, 2019
Permutation & Combination

A. Permutations/Arrangements

Each of the different arrangements which can be made by taking r things from n things is called permutation. The number of permutations (arrangements) of n dissimilar things taken r at a time is denoted by and is given by The number of permutations (arrangements) of n dissimilar things taken all at a time is

B. Combinations Selections

Each of the different groups of selections which can be made by taking r things from n things is called a combination

The number of combinations of n dissimilar things taken r at a time is denoted by is defined as

The number of combinations of n dissimilar things taken all at a time is

Problem Solving Trick

In a combination while forming a group or selection, we are only concerned with the number of things each group or selection contains while in a permutation, we are also concerned with the order of things which form the arrangements.

Selecting things without any order is called combination and Arrangement of things in Some Order is called Permutation

Important Illustration

Suppose out of three letters a, b and c we have to take two at a time. Then the combinations that can be formed are

ab, bc and ca

Problem Solving Trick

In a combination while forming a group or selection, we are only concerned with the number of things each group or selection contains while in a permutation, we are also concerned with the order of things which form the arrangements.

Selecting things without any order is called combination and Arrangement of things in Some Order is called Permutation

Important Illustration

Suppose out of three letters a, b and c we have to take two at a time. Then the combinations that can be formed are

ab, bc and ca

i.e. three combinations in all. It shoule be noted that ab and ba give the same combination because in Combination. The order of things is not important. SImilarly, bc and cb give same combination and ca and ac give the same combination

ab, ba, bc, cam ac

i.e. six permutations in all. Here, ab and ba are different permutations (arrangements) because in Permutation the order of things is important.

Problem Solving Trick

Working Rule to find the totality of All Permutations

Step I Firtst find all Combinations

Step II Then find all possible Arrangements that arise from each combination.

Step III Finally, the total of all arrangements in all combinations will give the totality of all permutations.

Complementary Combinations

If out of n things, we take r at a time, then automatically, we are left with a group of (n-r) things

Problem Solving Trick

In a combination while forming a group or selection, we are only concerned with the number of things each group or selection contains while in a permutation, we are also concerned with the order of things which form the arrangements.

Selecting things without any order is called combination and Arrangement of things in Some Order is called Permutation