using the letters in the word "MAGIC,", find the number of permutations that can be formed using 3 letters at a time
A. 20 , B. 30 , C. 40, D. 60
To find the number of permutations using 3 letters at a time from the word "MAGIC," we can use the formula for permutations:
P(n, r) = n! / (n - r)!
Where:
n = total number of letters in the word
r = number of letters chosen at a time
In this case, the word "MAGIC" has 5 letters (n = 5) and we want to choose 3 letters at a time (r = 3).
P(5, 3) = 5! / (5 - 3)!
= 5! / 2!
Calculating this:
5! = 5 x 4 x 3 x 2 x 1 = 120
2! = 2 x 1 = 2
Therefore:
P(5, 3) = 120 / 2 = 60
So, the number of permutations that can be formed using 3 letters at a time from the word "MAGIC" is 60.
The correct answer is D. 60.