You are the proud owner of a new social media website! You decide that you want your users to protect their accounts using a PIN. Two different security companies come to you:

Company A tells you that they can set up a 5 digit PIN where the first entry must be a capital letter (A to Z), the middle 3 entries must be integers (0 to 9), and the last entry must be a lowercase letter (a to z).

Company B tells you that they can set up a 4 digit PIN where each digit may be any lowercase letter (a to z) or integer from 0 to 9.

Using R, complete the following tasks:

(1): Use the expand.grid() function to create the sample space of possible PINs using Company A's plan. Call this sample space SA.

(2): Use the nrow() function to figure out how many possible PINs there are in SA

(3): Now look at Company B's plan. Create vector called entries that contains all the lowercase letter (a to z) and integer from 0 to 9. Then, using entries and expand.grid(), create the sample space of possible PINs using Company B's plan. Call this SB.

(4): There are four entries in the PIN this time, so there are 4 "stages." Each stage has the same number of options. The number of options per stage is 26 + 10 = 36, because there are 26 lowercase letters (a to z) and 10 digits (0 to 9).Using the product rule, the total number of possible PINs is 36 36 36 36 = 364 = 1, 679, 616. We will now check if this number is consistent with the size of SB. Use the nrow() function to figure out how many possible PINs there are in SB.