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8_murik_8 [283]
4 years ago
11

On day 1, i'm going to run 12 laps at the fitrec. then, for each of the next six days, i'm going to roll a six-sided die, and th

en run that many more laps than i ran the previous day. for example, i may end up running this sequence of laps: (12, 16, 21, 22, 23, 25, 30). how many different possible 7-day sequences of this form are there?
Mathematics
1 answer:
sveticcg [70]4 years ago
5 0
Short answer: 36.
This is a combination/permutation problem.
To put it simple, a die has 6 sides, there are 7 days but 1 is already determined (12 laps).
So if we multiple the options (sides on a die) × the number of days (6) we get:
6 × 6 = 36 possible outcomes.

To show this we can get
12, 13, 14, 15, 16, 17, 18
12, 13, 14, 15, 16, 17, 19
12, 13, 14, 15, 16, 17, 20
... all the way to
12, 18, 24, 30, 36, 42, 48
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a reflection over the x-axis and then a 90 degree clockwise rotation about the origin

Step-by-step explanation:

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