Example 3. How many ways are there to put m balls into n bins. Assume m ≤ n. 1. Balls are distinct and bins are distinct. Every ball has n choices. Hence n. Exercise 2. Why is the answer not m by looking at the opposite argument. 2. Balls are not distinct but bins are distinct. Take m identical balls and n− 1 identical sticks and permute them. Every permutation gives a different arrangement. So...

zygomycosis is a fulminant infection which usually afflicts patients who are immunocompromised by diabetes mellitus, malignancy or immunosuppressive therapy.l this disease is a rare but highly invasive fungal infection which occurs in organ transplant recipients. 2 mucormycosis confined to the gastrointestinal tract is an uncommon form of the disease. accounting for only seven percent of all mu...

introduction: the most important subcutaneous fungal infections in man are caused by injury due to contaminated thistles and thorns. from an epidemiological point of view , it is important to recognize the fungi as well as their frequency of them in various thistles and thorns methods: the present research has been conducted on thorns and thistles of 16 regions including cities and villages of ...

Shear-Thickening Fluids (STFs) are a special Non-Newtonian Fluid that act like a solid when they experience a force. A simple example of this is a mixture of cornstarch and water. In this experiment, I text this mixture’s STF properties by using a ball drop to simulate an impact. By varying the ball drop height (and thus the force upon impact), and observing the bounce height, I determined wher...

In this paper a four-ball-best-ball (4BBB) model for pairs of golf players is set up. The 4BBB match-play scoring system is seen to satisfy a basic requirement of fairness. It is shown that it is not strictly possible to rate individual players as 4BBB players. However, a (reasonably broad) class of individual players is identified such that it is possible to rate them individually as 4BBB play...

Ball Grid Array packages in which I/O pins are arranged in a grid array pattern realize a number of connections between chips and a printed circuit board, but it takes much time in manual routing. We propose a fast routing method for 2-layer Ball Grid Array packages to support designers. Our method obtains a via assignment which distributes wires evenly on top layer and has high completion rati...