10. Even and odd Fibonacci Numbers a.) Which of the Fibonacci numbers are even? What pattern do you see in the subscripts of the even ones? b.) Will the 30th Fibonacci number be even or odd? Explain how you know, using the pattern of the subscripts that you found. LOOKING UP or writing out up to the 30th Fibonacci number does not count as using the pattern! c.) Will the 100th Fibonacci number be even or odd? Explain how you can tell, using the pattern of the subscripts you found. LOOKING UP or writing out up to the 100th Fibonacci number does not count as using the pattern!
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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