Consider the following expanded powers of (a + b)n, where a + b is any binomial and n is a whole number. Look for patterns.
Each expansion is a polynomial. There are some patterns to be noted.
1. There is one more term than the power of the exponent, n. That is, there are terms in the expansion of (a + b)n.
2. In each term, the sum of the exponents is n, the power to which the binomial is raised.
3. The exponents of a start with n, the power of the binomial, and decrease to 0. The last term has no factor of a. The first term has no factor of b, so powers of b start with 0 and increase to n.
4. The coefficients start at 1 and increase through certain values about "half"-way and then decrease through these same values back to 1.
This is a fundamental counting principle problem and can be solved by multiplying the number of choices you have for each digit of the license plate.
For the first five digits you can choose from the numbers 0,1,2...,9 or 10 choices.
A we cannot repeat the digits, so, first five digits will be:
10 × 9 × 8 × 7 × 6
Now the next 1 digit will all be letter all being different
There are 26 letters in the alphabet.. for our second digit we have 26 choices,
Here is the whole calculation:
= 10 × 9 × 8 × 7 × 6 × 26
= 786240
To learn more about calculating possibilities from the given link
brainly.com/question/4658834
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