Questions # 4 , 6 and 8 Exercises for Section 3.2 1. Consider lists made from the

 

Questions # 4 , 6 and 8

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Exercises for Section 3.2 1. Consider lists made from the letters T, H, E, O, R, Y, with repetition allowed. (a) How many length-4 lists are there? (b) How many length-4 lists are there that begin with T? (c) How many length-4 lists are there that do not begin with T? 2. Airports are identified with 3-letter codes. For example, Richmond, Virginia has the code RIC, and Memphis, Tennessee has MEM. How many different 3-letter codes are possible? 3. How many lists of length 3 can be made from the symbols A, B, C, D, E, F if... (a) repetition is allowed. (b) (c) (d) ... repetition is not allowed. repetition is not allowed and the list must contain the letter A. repetition is allowed and the list must contain the letter A. 4. In ordering coffee you have a choice of regular or decaf; small, medium or large; here or to go. How many different ways are there to order a coffee? 5. This problem involves 8-digit binary strings such as 10011011 or 00001010 (i.e., 8-digit numbers composed of 0's and 1's). (a) How many such strings are there? (b) How many such strings end in 0? (c) How many such strings have 1's for their second and fourth digits? (d) How many such strings have 1's for their second or fourth digits? 6. You toss a coin, then roll a dice, and then draw a card from a 52-card deck. How many different outcomes are there? How many outcomes are there in which the dice lands on ? How many outcomes are there in which the dice lands on an odd number? How many outcomes are there in which the dice lands on an odd number and the card is a King? 7. This problem concerns 4-letter codes made from the letters A, B, C, D, ..., Z. (a) How many such codes can be made? (b) How many such codes have no two consecutive letters the same? 8. A coin is tossed 10 times in a row. How many possible sequences of heads and tails are there? 9. A new car comes in a choice of five colors, three engine sizes and two transmis- sions. How many different combinations are there? 10. A dice is tossed four times in a row. There are many possible outcomes, such as JBBJ, or 8000. How many different outcomes are possible? Exercises for Section 3.2 1. Consider lists made from the letters T, H, E, O, R, Y, with repetition allowed. (a) How many length-4 lists are there? (b) How many length-4 lists are there that begin with T? (c) How many length-4 lists are there that do not begin with T? 2. Airports are identified with 3-letter codes. For example, Richmond, Virginia has the code RIC, and Memphis, Tennessee has MEM. How many different 3-letter codes are possible? 3. How many lists of length 3 can be made from the symbols A, B, C, D, E, F if... (a) repetition is allowed. (b) (c) (d) ... repetition is not allowed. repetition is not allowed and the list must contain the letter A. repetition is allowed and the list must contain the letter A. 4. In ordering coffee you have a choice of regular or decaf; small, medium or large; here or to go. How many different ways are there to order a coffee? 5. This problem involves 8-digit binary strings such as 10011011 or 00001010 (i.e., 8-digit numbers composed of 0's and 1's). (a) How many such strings are there? (b) How many such strings end in 0? (c) How many such strings have 1's for their second and fourth digits? (d) How many such strings have 1's for their second or fourth digits? 6. You toss a coin, then roll a dice, and then draw a card from a 52-card deck. How many different outcomes are there? How many outcomes are there in which the dice lands on ? How many outcomes are there in which the dice lands on an odd number? How many outcomes are there in which the dice lands on an odd number and the card is a King? 7. This problem concerns 4-letter codes made from the letters A, B, C, D, ..., Z. (a) How many such codes can be made? (b) How many such codes have no two consecutive letters the same? 8. A coin is tossed 10 times in a row. How many possible sequences of heads and tails are there? 9. A new car comes in a choice of five colors, three engine sizes and two transmis- sions. How many different combinations are there? 10. A dice is tossed four times in a row. There are many possible outcomes, such as JBBJ, or 8000. How many different outcomes are possible?