irections 1. Solve the following problems. own paper. Do not write answers on th
ID: 3145976 • Letter: I
Question
irections 1. Solve the following problems. own paper. Do not write answers on this page. Show your work AND explain your reasoning using complete English sentences. Explanations must directly follow the solution for each part of the problem. Hand write your solutions and explanations on your 2. 3. You must write your name on the top right of the paper you turn in. 4. You must write the title of this problem set on the top of your paper. 5. Turn in your solutions following the directions in the assignment information on Blackboard. The formulae for the Sets and Counting Unit can be found in Blackboard under the Sets and Counting Unit. 4. Using the digits 0 through 9, find out how many 4-digit numbers can be configured based orn the stated conditions: a. The number cannot start with zero and no digits can be repeated. b. The number must begin and end with an odd digit. (Repeated digits are okay.) c. The number must be at least 5000 and be divisible by 10. (Repeated digits are okay.) d. The number must be less than 3000 and must be even. No digits may be repeated in the last 3 digits. (That is, 2234 would be okay, but 2334 would not be okay.) Grading Criteria 4. Total: 10 points a. Total: 3 points Breakdown Correct answer: 2 points Sentences explaining reasoning: 1 point b. Total: 2 point Breakdown Correct answer: 1 pointExplanation / Answer
4 (a)
four position
1st position : 9 choices
2nd position : 9 choices (because 1 digit has already been used in the first position and repeatition is not allowed and 0 has been added here)
3rd position : 8 choices
4th position : 7 choices
total numbers = 9*9*8*7 = 4536
(b)
1st position : 5 choices (only odd digits 1,3,5,7,9)
4th position : 5 choices (only odd digits 1,3,5,7,9)
2nd position : 10 choices (any digit)
3rd position : 10 choices (any digit)
total numbers = 5*5*10*10 = 2500
(c)
1st position : 5 choices (5,6,7,8,9)
2nd position : 10 choices
3rd position : 10 choices
4th position : 1 choices (only 0 can be here)
total numbers = 5*10*10*1 = 500
(d)
1st position : 2 choices (1,2)
4th position : 5 choices (even digits only)
2nd position : 9 choices
3rd position : 8 choices
total numbers = 2*5*9*8 = 720
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