For each of the five "slots" that we want to have for our password, we have ten different digits to choose from. The number of passwords is given by calculating  or  , which equals .

A three-letter-long password can be created in  ways, since there are 26 letters to choose from and the password is three letters long.

We are asked to find the number of ways in which the keys can be used on the locks. There are four keys and four locks. This is just like looking for the number of permutations of four different letters. Therefore, it is given by 4!

Indeed, if we start with the first lock, we have four keys, and if we only use the right key last, then we have made four attempts on the first lock. Assuming that we leave the key in the first lock, we then have three keys remaining for the second lock. Similarly, if we pick the wrong key twice, then the third opens the lock, and so on and so forth. We can then multiply all these possibilities  to obtain .

If a small pizza is chosen, one topping out of  can be ordered for no additional charge.

If a medium pizza is ordered, up to two different toppings out of  can be ordered for no additional charge - this is

If a large pizza is ordered, up to two different toppings can be ordered for no additional charge - again, this numbers .

Add these expressions:

Apply combinations and the multiplication principle here.

One possibility is to order three of three meats, which can only be done one way, and two of four vegetables, which can be done

 ways

The number of possible pizzas with three meats and two vegetables is .

The other possibility is to order two of three meats, which can be done 

 ways,

and three of four vegetables, which can be done 

 ways.

The number of possible pizzas with two meats and three vegetables is  ways.

This is a total of  ways to build a pizza to the given specifications.

There are  toppings overall. 

For a small pizza, since one topping is allowed, there are  possible choices.

For a medium pizza, there are 

ways to order two different toppings, and  ways to order a double topping. The same numbers hold for a large pizza.

Add these:

What is the 58th digit of the following repeating decimal?

Begin this problem by realizing there is an easier way than counting out to the 58th digit.

The easier way requires us  to divide 58 by the number of digits in the repeating decimal. In this case, we have 6.

So, perform the following:

9 remainder 4 means that the pattern will repeat 9 times before the 58th digit, and will then go 4 more. That means our answer must be 8, because 8 is the 4th digit in the sequence.

It can be solved by calculating all five answers:

The smallest is .

We need to convert this percentage into a fraction.  This is one of the conversions you should remember.

% = 0.666666 = 

It's easiest to convert the fractions into decimals.

Therefore, the correct answer is 0.25.