41,01,06,666.6666667 are possible combinations of a that license plate
Permutations and combinations are ways of representing groups of objects by selecting them and subsetting them into sets. It defines different ways of arranging a particular data group. When we choose data or objects from a particular group, it is called a permutation and the order in which they are presented is called a combination. Both concepts are very important in mathematics.
Let's assume the license plate has the 3 letters on the left hand side in a row, and the four letters on the right hand side in a row, like this:
AAA1234
We have have 26 possible letters to choose from, and we make this choice three times. So this gives us 26^3 possible letter combinations. Next, we have 10 single-digit numbers to choose from, and we make this choice 4 times. This gives us 10^4 possible number combinations. Multiplying these gives us 26^3×10^4 possible plates.
On the other hand, if there is no restriction on the placement of letters and numbers, we could have something like this:
A1A2A34B
But we can still only have 3 letters and 4 numbers.
So, to start out let's decide where to put our three letters. We need to pick 3 places out of 7, so thats (7/3) possibilities. Now that we have decided where to put our three letters, the other four spots must be numbers. At this point we have returned to our original problem where we know the positions of the letters and numbers. So the final answer should be
(7/3)×26^3×10^4 = 41,01,06,666.6666667 are possible combinations of a that license plate.
learn more about permutation and combination here :
brainly.com/question/28720645
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