California is coming out with a new license plate. the license plate will have 2 letters followed by 3 digits from 0 to 9 then followed by another letter. how many different license plates are possible if no letters and no digit repeat?

11,232,000 different plates

Step-by-step explanation:

Figure it out like this:

2letters × 3digits × 1letter

Nothing can repeat.  There are 26 letters in the alphabet.  If we use 1 of those letters, then there are only 25 letters left to choose from.  That's why we start with 26 × 25.

Now for the digits, we have 10 choices for the first digit, then 9 choices for the second digit, then 8 choices for the third digit.  That's why we follow the letters with 10 × 9 × 8.

For the last letter, we had 24 choices left, so the whole thing is found by multiplying:

26 × 25 × 24 × 10 × 9 × 8 × 24 = 11,232,000

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step-by-step explanation:

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb