How many words can be formed by using all the letters of word. ‘RAIN’?122412017

1. Break Down the Problem

We need to calculate the total number of distinct arrangements of the letters in the word "RAIN". The word consists of 4 unique letters: R, A, I, and N.

2. Relevant Concepts

The formula for calculating the number of distinct permutations of n unique items is given by:

$n! = n \times (n-1) \times (n-2) \times \ldots \times 1$

In this case, since there are 4 unique letters, we can represent the calculation as:

$4! = 4 \times 3 \times 2 \times 1$

3. Analysis and Detail

Now we will perform the calculations for $4!$:

1. $4! = 4 \times 3 = 12$
2. $12 \times 2 = 24$
3. $24 \times 1 = 24$

Thus, $4! = 24$.

4. Verify and Summarize

We have confirmed that the calculations are precise and that all letters in "RAIN" are unique. Therefore, the total number of distinct arrangements (words) that can be formed using all the letters of "RAIN" is indeed 24.

Final Answer

The total number of distinct words that can be formed by using all the letters of the word "RAIN" is 24.