How many 7-digit telephone numbers are possible if the first digit cannot be four and (a) only even digits may be used? (b) the number must be a multiple of 10 (that is, it must end in 0)? (c) the number must be a multiple of 100? (d) the first 2 digits are 26? (e) no repetitions are allowed?
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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