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fffbone
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Can anyone explain to me why k!/(k!*(k-k)!)+(k+1)!/(k!*(k+1-k)!)+(k+2)!/(k!*(k+2-k)!)+...+(n-1)!/(k!*(n-1-k)!)=n!/((k+1)!*(n-k-1)!) please. Thanks a lot!
A combination problem is a type of mathematical problem in which the order of the elements does not matter in the final solution. This means that the same set of elements can be arranged in different ways, resulting in multiple possible combinations.
To solve a combination problem, you need to identify the total number of elements and the size of each combination. Then, you can use the formula nCr = n! / (r! * (n-r)!) to calculate the number of combinations. Finally, you can list out all the possible combinations or use other techniques such as tree diagrams or the fundamental counting principle to find the solution.
A combination is a selection of elements where the order does not matter, while a permutation is a selection of elements where the order does matter. In other words, for a combination problem, "ABC" is considered the same as "BAC" or "CAB", while for a permutation problem, "ABC" is different from "BAC" or "CAB".
Combination problems can be found in various fields such as computer science, statistics, genetics, and probability. Some real-life applications include creating passwords, scheduling tasks, arranging genetic traits, and predicting outcomes of experiments or events.
One example of a combination problem is selecting a pizza with three toppings out of a menu of 10 toppings. In this case, the order of the toppings does not matter, and the number of possible combinations is 120 (10C3 = 10! / (3! * (10-3)!)). The combinations could be "pepperoni, mushrooms, olives", "sausage, onions, bell peppers", or "bacon, pineapple, jalapenos", among others.