A license plate is made of three letters and three numbers. How many different license plates are possible? (Recall there are 26 letters in the alphabet and 10 single digit numbers 0-9).

Using the permutations formula, it is found that: 11,232,000 different license plates are possible

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The order in which the letters and the numbers appear is important(123ABC is a different plate than A123BC), which means that the permutations formula is used to solve this question.

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Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

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In this question:

Thus:

11,232,000 different license plates are possible

A similar problem is given at link

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.