45697600 number of different license plates can be manufactured for this state.
What is Combination?
The combination is a mathematical technique that is the number of ways to arrange the n number of collections where the order of selection does not matter.
ⁿCₐ= n!/(n-a)!a!
Here given in the question,
On the license plate, there are 4 letters and 2 numbers.
There are 26 alphabets in English from A to Z for which at position 1, there are 26 possibilities of alphabets at every position by ²⁶C₁= 26!/(26-1)!1!= 26!/25!1!= 26!/25!= 26
So for 4 different positions of letters, the number of ways is = 26*26*26*26= 26⁴= 456976
There are 10 numbers in math for which at position 1, there are 10 possibilities of numbers at every position by ¹⁰C₁=10!/(10-1)!1!= 10!/9!1!= 10!/9!= 10
So for 2 different positions of numbers, the number of ways is = 10*10= 10²= 100
The total number of ways the license can be manufactured = 456976*100= 45697600
Therefore 45697600 different license plates can be manufactured for this state.
Learn more about the combination
here: https://brainly.com/question/11732255
#SPJ2
