Use two red squares and one green square. How many distinct ways can you arrange

Question

Use two red squares and one green square. How many distinct ways can you arrange these three squares in a row? Record each arrangement as you make it. b. If all the squares in Part a had been different colors, how many arrangements would have been possible? c. The number of arrangements in Part a is what fraction of the number in Part b? How is this fraction related to the number of red squares? d. Explain why the number of arrangements of two red squares and one green square should be this fraction of the number of arrangements of three squares.

Explanation / Answer

1. a.The different arrangements are:

Red-Red-Green

Red-Green-Red

Green-Red-Red

Thus there are 3 different arrangements.

b. The first place can be occupied by one of the three squares.

The second place can be occupied by one of the two remaining squares.

The third place can be occupied by only the remaining square.

Thus total number of arrangements = 3*2*1 = 6.

c. Number of arrangements in a / Number of arrangements in b

= 3/6 = 1/2.

This is equal to the reciprocal of the number of red squares in a. It is also four times the number of red squares in a.

d. A red square is replaced by square of the other number. Thus every repeated arrangement (there are 2 of them as there are 2 red squares) will now be considered a new arrangement. As a result there will be twice the number of arrangements.

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