Internal telephone numbers in a university are composed of 5 digits. The first two digits can form any integer between (and including) 61 and 75, the third digit is an integer between 1 and 9, and the last two each take any integer value. Assume that it is disallowed to have a phone number with the last three digits being 999, 995, 911, or 100. What is the total number of possible internal telephone numbers that start with the digit 6?
Part A) Internal telephone numbers in a university are composed of 5 digits. The first two digits can form any integer between (and including) 61 and 75, the third digit is an integer between 1 and 9, and the last two each take any integer value. Assume that it is disallowed to have a phone number with the last three digits being 999, 995, 911, or 100.
What is the total number of possible internal telephone numbers that start with the digit 6?
Part B) A system is composed of 6 components (A, B, C, D, E, F), each of which is either working or failed. The probability that a component is working is 0.54. Suppose the system will work if components A and B are both working, or if components E and F are both working. Find the probability that the system is working.
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