Counting numbers are to be formed using only the digits 6, 7, and 8. Determine the number of different possibilities for the type of number described below. Four-digit numbers with one pair of adjacent 6s and no other repeated digits (Hint: You may want to split the task of designing such a number into three parts, such as (1) position the pair of 6s, (2) position the 7, and (3) position the 8.) The number of different possibilities for this type of number is. (Type a whole number.)
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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