The total combinations of license plates possible in the state are 17,576,000.
What is Permutation?
The act of organizing all the components of a set into some sequence or order is known as permutation. Permuting, in other words, is the act of reordering the components of a set that has previously been sorted.
A permutation is the selection of r items from a collection of n items without replacement, with the order of the items being significant.
nPr = (n!) / (n-r)!
What is a Combination?
The combination is a method of picking elements from a collection in which the order of selection is irrelevant (unlike permutations).
A combination is a selection of r items from a collection of n items with no replacements and no regard for order.
nCr = (n!)/{(r!)((n-r)!)}
How do we solve the given question?
We are given that each license plate in a certain state has six characters (with repeats allowed).
Here are the possibilities for each character.
Character
Possibilities
First
The 26 letters of the alphabet
Second
The 26 letters of the alphabet
Third
The 26 letters of the alphabet
Fourth
The 10 digits 0 through 9
Fifth
The 10 digits 0 through 9
Sixth
The 10 digits 0 through 9
We are asked to find how many license plates are possible in this state.
We first check the number of combinations for each character and then multiply them all to get the total number of license plates possible.
First character: 26 (∵ All the 26 letters are possible, so the combinations are 26P1 = 26).
Second character: 26 (∵ All the 26 letters are possible, so the combinations are 26P1 = 26).
Third character: 26 (∵ All the 26 letters are possible, so the combinations are 26P1 = 26).
Fourth character: 10 (∵ All the 10 digits are possible, so the combinations are 10P1 = 10).
Fifth character: 10 (∵ All the 10 digits are possible, so the combinations are 10P1 = 10).
Sixth character: 10 (∵ All the 10 digits are possible, so the combinations are 10P1 = 10).
∴ Total number of license plates possible in the state = 26*26*26*10*10*10 = 26³*10* = 17576*1000 = 17,576,000
∴ The total combinations of license plates possible in the state are 17,576,000.
Learn more about permutations and combinations at
brainly.com/question/4658834
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