character in a password is either a digit [0-9] or lowercase letter [a-z]. How many valid passwords are there with the given restriction(s)? The length is 17.

The number of unique arrangements of all the letters in the word CONDOMINIUM is: 39 916 800 19 958 400 2 494 800 990

Users of the online system for a Bank are required to set a password that is 10 character-long. Each character can be a letter, a 1-digit number, or a symbol from the list: !, @, #, &, % How many passwords are possible if there is no distinction between upper case and lower case letters? (Not Case-sensitive) How many passwords are possible if the first and last digits have to be numbers?

A standard-issue 2020 New Jersey license plate had one letter, then two digits, followed by three letters. New Jersey DOO SPA Garden State These plates were not allowed to have letters D, T, or X in the fourth position, or the letters I, O, or Q in any position. With these restrictions, how many different license plates were possible in 2020?

Evaluate the combination. C(38,30) C(38,30) = (Use scientific notation. Round to three decimal places as needed. Use the multiplication symbol in the math palette as needed.)

In the game of poker played with an ordinary deck of 52 cards various five-card holdings are given special names. The name "three of a kind" is reserved for a holding that meets the following rule: Three cards of the same denomination and two other cards of different denominations. The number of distinct "three of a kind" that can be drawn from a 52-card deck can be calculated with the following product expression: 030² Explain what each of the factors in the expression represents in terms of selections from the deck of cards. Follow the examples given in slides 8-10 of the lecture Section 9.5 Combinations.pdf.

4. Determine the following commutators: d? d Px»