How many different words can be formed using all the letters of the word "SPECIAL", so that the

step 1 So this is question number 15 and here it says that how many different words can be formed using

How many different words can be formed using all the letters...

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Key Concepts

Fundamental Counting Principle

The fundamental counting principle states that if one event can occur in m ways and another independent event can occur in n ways, then the total number of ways both events can occur is m multiplied by n. This principle is used to combine the number of arrangements for independent subsets of items.

Permutations

Permutations refer to the different arrangements that can be made from a set of items, where the order of the items is important. This concept is essential when determining how many ways a group of distinct elements, such as letters, can be organized.

Positional Constraints

Positional constraints involve restrictions on where certain elements can be placed within an arrangement. This entails designating specific positions (like odd or even positions) for a subgroup of elements, which limits the overall number of valid arrangements.

Factorial Notation

Factorial notation (n!) represents the product of all positive integers from 1 to n, and is used to count the number of ways to arrange n distinct items. It is a fundamental tool in calculating permutations and is often applied separately to different subsets of elements in problems with restrictions.

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