in how many ways can be the first four letters of your name be arranged to form a three letter word,
(i)when the letter can be repeated
(ii)when the letter can not be repeated
E D W A
as a 3-letter "word" = 4x4x4 = 64 ways if the letters can be repeated
and 4x3x2 or 24 ways if the letters cannot be repeated.
To find the number of ways the first four letters of your name can be arranged to form a three-letter word, we can use the concept of permutations.
(i) When the letters can be repeated:
In this case, we can have the same letter used multiple times in the word.
To find the number of arrangements, we need to calculate the number of permutations with repetition. We can use the formula:
n^r
where n is the number of options (letters in this case) and r is the number of positions to fill.
In this scenario, as we have four letters in the first four positions and three positions to fill in the word:
Number of arrangements = 4^3 = 64
Therefore, when the letter can be repeated, there are 64 different ways the first four letters of your name can be arranged to form a three-letter word.
(ii) When the letters cannot be repeated:
In this case, each letter can only be used once in the word.
To find the number of arrangements, we need to calculate the number of permutations without repetition. We can use the formula:
P(n, r) = n! / (n - r)!
where n is the number of options (letters in this case) and r is the number of positions to fill.
In this scenario, as we have four letters in the first four positions and three positions to fill in the word:
Number of arrangements = 4! / (4 - 3)! = 4! / 1! = 4 * 3 * 2 = 24
Therefore, when the letter cannot be repeated, there are 24 different ways the first four letters of your name can be arranged to form a three-letter word.