A set of angles has a ratio of 5 to 2. If the larger angle measures 105 degrees then what is the measure of the smaller angle
2 answers:
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Answer:
a) 20 different arrangements
b) 10 different arrangements
Step-by-step explanation:
When the order of selection is significant, we utilize permutations to determine the number of arrangements; if the order does not matter, we apply combinations.
For part a)
We must select 2 items from a collection of 5, considering that order matters. This is a permutation scenario, thus we calculate 5P2.
The general formula for permutations of n items taken r at a time is:
By inserting n=5 and r=2, we have:
Hence, it is possible to select 2 items from a group of 5 when the selection order is relevant.
For part b)
Since the order of selection is unimportant, we use combinations to calculate the number of ways of selecting 2 items from 5, represented as 5C2.
The general formula for combinations of n items taken r at a time is:
Plugging n=5 and r=2 into the formula results in:
This demonstrates that we can choose 2 items from a collection of 5 when the order of selection is not significant.