Answer the questions below. (If necessary, consult a list of formulas.) (a) To log on to a certain computer account, the user must type in a 4-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4-letter passwords are possible? (There are 26 letters in the alphabet.) \( \square \) \( \begin{array}{l}\text { (b) There are } 17 \text { appetizers available at a restaurant. From these, Raina is to choose } 12 \text { for her } \\ \text { party. How many groups of } 12 \text { appetizers are possible? } \\ \square\end{array} \)

For the 4-letter password, since no letter may be repeated, the calculation is as follows: you have 26 options for the first letter, 25 for the second, 24 for the third, and 23 for the fourth. So, the total number of possible passwords is: \[ 26 \times 25 \times 24 \times 23 = 358,800 \] For the appetizers, since the order in which they are chosen does not matter, you would use combinations. The formula for combinations is given by \( \binom{n}{r} \), where \( n \) is the total number of options (17 appetizers), and \( r \) is the number to choose (12 appetizers). This can be calculated as: \[ \binom{17}{12} = \binom{17}{5} = \frac{17!}{5! \cdot (17 - 5)!} = 6188 \] So Raina has 6188 different groups of appetizers to choose from!