Depreciation Given the choice, would a firm prefer to use MACRS depreciation or straight-line… Depreciation Given the choice, would a firm prefer to use MACRS depreciation or straight-line depreciation? Why? Q

The probability that exactly three individuals have the same birthday and the rest have different birthdays can be calculated as follows: First, choose a specific day (out of the 365 possible birthdays) for the three individuals to share. The probability of this occurring is 1/365. Next, choose these three individuals from the group of n. This can be done in (n choose 3) ways. For the remaining n-3 individuals, we must assign them each a different birthday than the one already chosen. The first individual has a probability of 364/365 of having a different birthday, the second has a probability of 363/365, and so on. Therefore, the probability of the remaining individuals having different birthdays is: (364/365) x (363/365) x ... x [(366-n)/365] Multiplying these probabilities together, we get: P(exactly 3 matching birthdays) = (n choose 3) x (1/365) x (364/365) x (363/365) x ... x [(366-n)/365] For n = 40, we have: P(exactly 3 matching birthdays) = (40 choose 3) x (1/365) x (364/365) x (363/365) x ... x (326/365) Using a calculator, this comes out to \approx imately 0.008. Therefore, the probability that in a group of 40 randomly selected individuals, exactly three have the same birthday and there are no other matching birthdays is \approx imately 0.008.