A large bank vault has several automatic burglar alarms. The probability is 0.55 that a single alarm will detect a burglar. n USE SALT (a) How many such alarms should be used to be 99% certain that a burglar trying to enter is detected by at least one alarm? (Enter the smallest number of alarms needed to be at least 99% certain.) alarms (b) Suppose the bank installs nine alarms. What is the expected number of alarms that will detect a burglar? alarms

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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.

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The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.