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A Give three 5-letters words with repeating letters. How many unique arrangements can be
made of those letters?
1
2
3
B. Write 2 simple word problems about solving problem involving permutation Write the
solution to the problem.
4
5

Question

Answered

Sagot :

Chakc234id Chakc234id · Answer 1

Answer:

There exist 2 cases to consider :

Case 1 - The two O's are not identical

Then it is equivalent to asking in how many different ways can 5 different units be arranged in a row.

This is simply

5

!

=

120

different ways.

Case 2 - The two O's are identical

This is then equivalent to asking in how many different ways can 5 items be arranged in a row, if 2 of the 5 items are identical.

By the addition principle, there are 10 possible ways to place the 2 identical objects in the 5 available slots in the row.

Now for each of these 10 different arrangements of the identical items, the other 3 non-identical items may be placed and arranged in

3

≠

6

different ways.

So in total, there are then

6

×

10

=

60

different ways.

Note that since the 2 identical objects can themselves be arranged in

2

!

different ways, we don't include this in the total since these arrangements are considered identical to one of the others already.