Nick is writing the 4 letters in his name in different orders. In how many orders can he put the letters?
use permutations and combinations on these types of problems.
number of arrangements
= 4x3x2x1 = 4! = 24
each letter can be written in many ways just use the # of arrangements
To determine the number of ways Nick can arrange the 4 letters in his name, we can use the concept of permutations.
In permutation, the formula to find the number of arrangements of n objects is n!.
The exclamation mark represents the factorial operation. In this case, n! means the factorial of the number of objects, which is the product of all positive integers from 1 to n.
For Nick's name, since there are 4 letters, we can find the number of arrangements using the formula:
4! = 4 x 3 x 2 x 1 = 24
Therefore, Nick can put the letters of his name in 24 different orders.