Exponential generating function of the partitions
Determine the exponential generating function of the partitions of the set [n], all of whose classes have a prime number of elements.
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Find out the singular points of the equation (x^2 + 2x)^2 Y" - 4xY' +5Y = 0 and classify them as regular or irregular.
There're 20 people sitting in waiting room. The usher in charge should select 5 of these people to go to the green sanctuary and 3 of these people to go to the red sanctuary. In how many different manners can the usher do this? The standard answer
It is well known that infants born to mothers who smoke tend to be small and prone to the range of ailments. It is conjectured that also they look abnormal.
In a ballroom dance class, participants are divided in couples for each drill session. One partner leads and other follows for three minutes, and then the couple switches roles for next three minutes.
Determine the present value of ordinary annuity which has payments of $1100 per year for 19 years at 5% compounded annually.
Dystopia county has three bridges. In the next year, Elder bridge has 11% chance of collapse, the Younger bridge has 4% chance of collapse, and the Ancient bridge has 20% chance of collapse. Determine the probability that exactly one of such bridg
An oil company is drilling for oil at three sites. According to the geological tests, the probabilities of determining oil at these three sites are 0.30, 0.15, and 0.20, respectively.
You're using an unreliable Wi-Fi connection. You send three emails - one to your bank, one to magazine, and one to your professor. Each email has a 30% chance of going through, independently of whether other emails go through. Determine the chance
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