Question

Find the number of permutations of letters in the word SHANTARAM. *​

Answer 1

A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

For example, suppose we have a set of three letters: A, B, and C. We might ask how many ways we can arrange 2 letters from that set. Each possible arrangement would be an example of a permutation. The complete list of possible permutations would be: AB, AC, BA, BC, CA, and CB.

When they refer to permutations, statisticians use a specific terminology. They describe permutations as n distinct objects taken r at a time. Translation: n refers to the number of objects from which the permutation is formed; and r refers to the number of objects used to form the permutation. Consider the example from the previous paragraph. The permutation was formed from 3 letters (A, B, and C), so n = 3; and the permutation consisted of 2 letters, so r = 2.

In the word 'SHANTARAM', the number of letters is

n = 9, of which A repeats thrice, i.e., p = 3 and rest are distinct.

You're welcome,

Primrose Omega.