Tallerent from the member of ways to arrange themselves in a line try to wins to your advantage to cut down on the amount of work involved. 3. Use the multiplication, complementary, and/or addition counting principles to obtain the number of possible ways in which the following events can occur. (a) A combination lock requires the entry of three numbers each from 1 through 30. If numbers can be repented, how many distinct combinations are possible? Note: 1-2-3 is distinct from 2-1-3, for example. (b) A bank signs randomly generated 4-character (alphanumeric) PINs with its debit cards. However, since their ATM keypad is as seen below, many different PINs will share the same key sequence (for example, 2133, AZDE, and BQ3F are all keyed in exactly the same way). How many different PINS are represented by the same sequence of keys as 52197 7103? O (c) In the first episode of a new reality TV show & sociopaths will be paired up with 8 psychopaths. How many ways can this be done? (d) Suppose that Rhode Island currently has an automated system that randomly generates seven-character alphanumeric combinations for its license plates Tired of dealing with letterumber confusion (people mistaking 2's for Z's, etc.) and realizing that the current population doesn't require so much variation the state is considering moving to a six-character string made up of a three letter combinntion followed by a three digit combination. How many distinct plates can the current system produce? How many can the proposed system produce? mu Users/Alzou/Downloads/260 h alphanumeric combinations for its license plates. Tired of dealing with letter number confusion (people mistaking 2's for Z's, etc.) and realizing that the current population doesn't require so much variation, the state is considering moving to a six-character string made up of a three letter combination followed by a three digit combination. How many distinct plates can the current system produce? How many can the proposed system produce? (e) How many times will the function in the innermost loop be called when the algorithm is run? for i-2 to 9 for j=10 to 20 for k=25 to 34 awesome Function(ij,k) end end end (f) How many ways can the letters of the word COMPLEX arranged in a row if E and X must remain next to each other as either EX or XE? (g) How many integers from 1 through 100,000 contain the digit 6 at least once? (h) How many integers from 1 through 1,000 are multiples of 4 or 7? (i) An early BASIC compiler recognized variable names according to the following rules: Numeric variable names had to begin with a letter and this letter could then be followed by another letter or a digit or by nothing at all. String variable names had to begin with the symbol $ followed by a letter, which could then be followed by another letter or a digit or by nothing at all. How many distinct variable names were recognized by this BASIC compiler? . - 00) ENG o 03:18 PM 11/23/2020 Bi Tallerent from the member of ways to arrange themselves in a line try to wins to your advantage to cut down on the amount of work involved. 3. Use the multiplication, complementary, and/or addition counting principles to obtain the number of possible ways in which the following events can occur. (a) A combination lock requires the entry of three numbers each from 1 through 30. If numbers can be repented, how many distinct combinations are possible? Note: 1-2-3 is distinct from 2-1-3, for example. (b) A bank signs randomly generated 4-character (alphanumeric) PINs with its debit cards. However, since their ATM keypad is as seen below, many different PINs will share the same key sequence (for example, 2133, AZDE, and BQ3F are all keyed in exactly the same way). How many different PINS are represented by the same sequence of keys as 52197 7103? O (c) In the first episode of a new reality TV show & sociopaths will be paired up with 8 psychopaths. How many ways can this be done? (d) Suppose that Rhode Island currently has an automated system that randomly generates seven-character alphanumeric combinations for its license plates Tired of dealing with letterumber confusion (people mistaking 2's for Z's, etc.) and realizing that the current population doesn't require so much variation the state is considering moving to a six-character string made up of a three letter combinntion followed by a three digit combination. How many distinct plates can the current system produce? How many can the proposed system produce? mu Users/Alzou/Downloads/260 h alphanumeric combinations for its license plates. Tired of dealing with letter number confusion (people mistaking 2's for Z's, etc.) and realizing that the current population doesn't require so much variation, the state is considering moving to a six-character string made up of a three letter combination followed by a three digit combination. How many distinct plates can the current system produce? How many can the proposed system produce? (e) How many times will the function in the innermost loop be called when the algorithm is run? for i-2 to 9 for j=10 to 20 for k=25 to 34 awesome Function(ij,k) end end end (f) How many ways can the letters of the word COMPLEX arranged in a row if E and X must remain next to each other as either EX or XE? (g) How many integers from 1 through 100,000 contain the digit 6 at least once? (h) How many integers from 1 through 1,000 are multiples of 4 or 7? (i) An early BASIC compiler recognized variable names according to the following rules: Numeric variable names had to begin with a letter and this letter could then be followed by another letter or a digit or by nothing at all. String variable names had to begin with the symbol $ followed by a letter, which could then be followed by another letter or a digit or by nothing at all. How many distinct variable names were recognized by this BASIC compiler? . - 00) ENG o 03:18 PM 11/23/2020 Bi