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How to solve permutation problems – repetition concept?

Permutation Problems ask you to arrange number of items into groups in a specific way. We see how items are arranged into groups and what is meaning of arranging them in a specific way? Answer of these two questions will give you answer the question how to solve permutation problems using repetition concept? In Permutation Problems you will repeatedly encounter a situation that will ask you to arrange n items in m number of ways and the order of the arrangement will either be given or hidden. If it is given in Permutation Problems and the order is significant it means that the math question is asking about Permutation and you have to concentrate on how to solve permutation problems? If Permutation problems are silent about significance of order, you’ll have to recognize it using your intelligence. Whatever the case be, you are going to solve Permutation Problems using repetition concept.

Now see following example to find answer of how to solve permutation problems using repetition concept?

Example

Suppose you are 5 friends and 2 chairs are available. In how many ways you 5 friends can seat in 2 chairs?

Solution

See in this Permutation Problem nothing has been mentioned about order of significance. Now you have to recognize significance of order. But the question is how to recognize significance of order where it is not mentioned in Permutation Problems.

Suppose A, B, C, D, E are 5 friends. You have to arrange them into group of 2. Now we can arrange them into following ways.

AB AC AD AE
BA BC BD BE

Note difference in seating positions AB and BA. A is to the left in the former while to the right in the latter. Though there is repetition of A and B in both seating positions but we cannot ignore this repetitive arrangement as it makes a new seating arrangement. It means repetition is allowed here. So they can seat in 8 ways.

Remember, in Permutation Problems repetition is allowed. First, recognize whether repetition is allowed, if it is allowed then contemplate on how to solve permutation problems. If repetition is not allowed then think around how to solve combination problems?

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