How many distinct four digit numbers contain the digits 1,2,3, and 4 without repetition, if the digit 2 is always immediately followed by the digit 3?

6

Step-by-step explanation:

If the question were how many distinct four digit number contain the digits 1,2,3, and 4 without repetition we could use the variation without repetition formula for 4 elements.

The first digit must be any of this four digits, so, we have 4 possibilities.

For the second digit, we already used one digit, so, we only have 3 possibilities. The total possibilities of picking this first two numbers are 4 * 3.

For the third digit, we already used two digits, so, we have 2 possibilities. The total possibilities thus far are then 4 * 3 * 2.

And for the final digit we don't have a choice, its the only one left. So we have 4 * 3 * 2 * 1 possibilities for a four digit number formed by the digits 1,2,3, and 4  without repetition .

This number its the factorial of 4:

.

If the digit 2 is always immediately followed by the digit 3, no, we don't have 4 choices, cause, our elements are:

the digit 1 , the duple 2 3 , and the digit 4

So, for the first position, we must choose one of this elements. Lets say 1.

1 _ _ _.

Then, we can choose the duple 23 for the second and third position:

1 2 3 _

Finally we only got one choice, the digit 4:

1 2 3 4

So, as we can see. This is the same that choosing three elements without repetition. The possibilities will be:

.

Now, we could: ask which are this possibilities?. They are:

1 2 3 4

1 4 2 3

2 3 1 4

2 3 4 1

4 1 2 3

4 2 3 1

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

step-by-step explanation:

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