Suppose we want to form three-digit numbers using the set of digits [0,1,2,3,4,5). For example, 501 and 224 are such numbers but 035 is not. (a) How many such numbers are possible? (b) How many of these numbers are multiples of 5? (c) If one three-digit number is chosen at random from all those that can be made from the above set of digits, find the probability that the one chosen is not a multiple of 5
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.
Suppose we want to form three-digit numbers using the set of digits [0,1,2,3,4,5). For example, 501 and 224 are such numbers but 035 is not. (a) How many such numbers are possible? (b) How many of these numbers are multiples of 5? (c) If one three-digit number is chosen at random from all those that can be made from the above set of digits, find the probability that the one chosen is not a multiple of 5
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