The appropriate method to use in solving the given question is permutation. Then, the numbers of ways to arrange the buttons is 1320 ways.

In the given question, the order of arrangement is important, so that the number of ways that Fiona could order the buttons can be determined by permutation method.

i.e $_{n}$ $P_{r}$ = $\frac{n!}{(n - r)!}$

Red 6

Green 3

Yellow 3

Total 12

Since no two neighbouring buttons of the same colour is allowed, then 3 buttons would be arranged at a time.

Thus, n = 12 and r = 3;

$_{12}$ $P_{3}$ = $\frac{12!}{(12 - 3)!}$

= $\frac{12!}{9!}$

= $\frac{12*11*10*9!}{9!}$

= 12 x 11 x 10

$_{12}$ $P_{3}$ = 1320

Therefore the buttons can be arranged in 1320 ways without two neighbors having the same colour.

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3 0

3 years ago

Read 2 more answers

Convert the unit of capacity.<br> 9 qt 3 cequals___ fl oz<br><br> 20 points

pickupchik [31]

Answer: The answer is 288

Step-by-step explanation:

5 0

3 years ago

Is 5.26 a rational or irrational number

kolbaska11 [484]

5.26 is equivalent to 526/1000, which is the ratio of two integers. 526/1000 can, in turn, be reduced to 263/500, which is the same (ratio). Thus, 5.26 is rational.

7 0

3 years ago