Question

A 1×6 square unit rectangular grid has to be covered with six 1×1 square unit tiles. Three of the tiles are yellow, two are white, and one is blue. In how many ways can this task be done if
b

no two neighboring tiles are the same color?

Answer 1

Answer:

1x6

Step-by-step explanation:

Answer 2

The number of ways the task of Rearranging the rectangular grid can be done if no two neighboring tiles are the same color is;

P(no two neighboring tiles are same) = 60 ways

We are given;

Number of yellow tiles; n_y = 3

Number of white tiles; n_w = 2

Number of blue tiles; n_b = 1

Now, if no two neighboring tiles can be the same tile Color, it means that;

P(no two neighboring tiles are same) = number of ways when no restriction/((n_y)! × (n_w)! × (n_b)!)

>> P(no two neighboring tiles are same) = 6!/(3! × 2! × 1!)

>> P(no two neighboring tiles are same) = 720/12

P(no two neighboring tiles are same) = 60 ways

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