With  selections made from  potential options, the total number of possible combinations (order doesn't matter) is:

The number of combinations increases the closer the value of  is to .

In the case of  being even:

In the case of  being odd:

When a value of  drifts farther from these values, the number of potential combinations decreases to a minimum of .

Note that for an odd , consider the difference small values of   and the smaller , and the difference of large values of   and the larger .

Since there are 37 options, an odd number:

For the potential numbers of purchased sweaters:

Note that nineteen also corresponds to the maximum number of possible combinations.

 gives the smallest amount of potential combinations for the choices presented.

With  selections made from  potential options, the total number of possible combinations (order doesn't matter) is:

The number of combinations increases the closer the value of  is to .

In the case of  being even:

In the case of  being odd:

When a value of  drifts farther from these values, the number of potential combinations decreases to a minimum of .

Note that for an odd , consider the difference small values of  and the smaller , and the difference of large values of  and the larger .

Since  is even:

 is farthest from  and gives the least amount of possible combinations.

Since in this problem the order of selection does not matter, we're dealing with combinations.

With  selections made from  potential options, the total number of possible combinations is

Quantity A:

Quantity B:

The two quantities are equal.

Since in this problem the order of selection does not matter, we're dealing with combinations.

With  selections made from  potential options, the total number of possible combinations is

Since Bryant is buying three basketballs from a selection of seven, the number of possible combinations is

Since in this problem the order of selection does not matter, we're dealing with combinations.

With  selections made from  potential options, the total number of possible combinations is

One option is chosen from the ten entrees, so the number of entree combinations is

Two options are chosen from the six sides, so the number of side combinations is

The total number of combinations is the product of these individual results:

We want to move the decimal point to the place just after the first non-zero number, in this case 6, and then drop all of the non-significant zeros. We need to move the decimal point five spaces to the right, so our exponent should be negative.  If the decimal had moved left, we would have had a positive exponent.  

In this case we get 6.009 * 10^–5.

We need to convert  into a number of the form .

The trick is, however, figuring out what  should be. When you have to move your decimal point to the right, you need to make the decimal negative. (Note, though, when you multiply by a negative decimal, you move to the left. We are thinking in "reverse" because we are converting.)

Therefore, for our value, . So, our value is:

The easiest way to do this is to convert each of your answer choices into scientific notion and compare it to .

For each of the answer choices, this would give us:

 (Which is, thus, the answer.)

When you convert, you add for each place that you move to the left and subtract for each place you move to the right. (Note that this is opposite of what you do when you multiply out the answer. We are thinking in "reverse" because we are converting.)

To add decimals, simply treat them like you would any other number.  Any time two of the digits in a particular place (i.e. tenths, hundredths, thousandths) add up to more than ten, you have to carry the one to the next greatest column.  Therefore:

So .

To solve this problem, subtract  from both sides of the eqution, 

Therefore, .

If you're having trouble subtracting the decimal, mutliply both numbers by  followed by a number of zeroes equal to the number of decimal places.  Then subtract, then divide both numbers by the number you multiplied them by.