Seven times the sum of 5 and a number amount to 91. Find the number
2 answers:
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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 =
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 x 11 x 10
= 1320
Therefore the buttons can be arranged in 1320 ways without two neighbors having the same colour.
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If we want to compute , we have to substitute every occurrence of
with
in the definition of the function:
Similarly, computing means to substitute the input with 2:
So, we have
And finally