In how many ways can the letters of the word EIGHT be arranged using only four of the letters at a time?
combinations of 5 letters taken four at a time
= 5!/[4! (5-4)!] = 5
The letters are to be arranged, so order matters.
number of ways = 5x4x3x2 = 120
120
48
To find the number of ways the letters of the word EIGHT can be arranged using only four of the letters at a time, we can apply the concept of permutations.
First, let's determine the total number of possible arrangements of the word EIGHT. Since EIGHT has five letters, there are 5 options for the first position, 4 options for the second position, 3 options for the third position, 2 options for the fourth position, and 1 option for the fifth position. Thus, the total number of possible arrangements of EIGHT is calculated as:
5 x 4 x 3 x 2 x 1 = 120 ways.
However, we only want to consider arrangements using four of the letters at a time. In other words, we need to select four letters out of the five. This can be calculated using the concept of combination.
The number of ways to choose four letters out of five can be calculated as:
5! / (4!(5-4)!) = (5 x 4 x 3 x 2 x 1) / ((4 x 3 x 2 x 1) x (1)) = 5 ways.
Therefore, there are 5 ways to arrange the letters of the word EIGHT using only four of the letters at a time.