According to a survey, 63% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly selected, and the number cleared by arrest or exceptional means is recorded. (a) Find the probability that exactly 40 of the murders were cleared. (b) Find the probability that between 36 and 38 of the murders, inclusive, were cleared. (c) Would it be unusual if fewer than 18 of the murders were cleared? Why or why not? (a) The probability that exactly 40 of the murders were cleared is. (Round to four decimal places as needed.)

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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.