1) Evaluate the expression. Determine the number of combinations of 7 things taken 4 at a time. (4 points) 2) Solve the problem. Mark can remember only the first 4 digits of his friend\'s phone number. He also knows that the number has 7 digits and that the last digit is not a 0. If Mark were to dial all of the possible numbers and if it takes him 21 seconds to try each one, how long would it take to try every possibility? (7 points) 3) Solve the problem. Four accounting majors, two economics majors, and three marketing majors have interviewed for five different managerial positions with a large company. Find the number of different ways that five of these people could be hired if the first two positions are to be filled by an accounting manager and an assistant accounting manager, the third position is to be filled by an economics manager, and the last two positions are to be filled by a marketing manager and an assistant marketing manager. (7 points) 4) Find the indicated probability. A bag contains 5 red marbles, 4 blue marbles, and 1 green marble. If a marble is selected at random, what is the probability that it is not blue? (7 points)
1) 7C4=7! / 4!(7-4)! = 7! / ( 4! * 3! ) = 5040 / (24*6) = 35
2) Mark doesn\'t know 3 out of the 7 digits and each digit has 10 possibilities except the last one which has 9 because 1-9 (1 to 9) leaving 0. If he goes through every possible combination it will take 10*10*9*21 seconds. That is 18900 seconds
3) We are going to use permutation instead of combination here because one is a manager and other is an assistant manager due to which the position of the majors matters while getting the job.
Hence for two accounting position 4P2 and for one economics manager 2C1 and for two marketing managers 3P2 . We used combination for economics manager because the position doesn\'t matter in this case.
Hence 4P2 * 2C1 * 3P2 = 12 * 2 * 6 = 144
4) P(not blue) = number of marbles which is not blue / number of total marbles
= (5+1)/10
=6/10
= 0.6
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