The total number of rings available for selection is 1350.
The combination is a process of knowing the number of ways of selecting a smaller set of articles from a larger set of articles where the order of selection is invariant.
If we select r items from n items in no particular order, the number of ways of doing so is calculated using combinations by the formula:
nCr = n!/{ r! (n - r)! }.
In the question, we are given that to order a class ring, students must decide on gold, silver, or white gold band and one of 15 stones. They must also choose from one of 30 activity symbols to put on the side.
We are asked the number of different ring selections there.
For the band:
Options available, n = 3.
Options to select, r = 1.
Thus, using combinations, the number of ways of selecting 1 band from 3 bands = 3C1 = 3!/{1! (3 - 1)! } = 3!/1!2! = 3.
For the stone:
Options available, n = 15.
Options to select, r = 1.
Thus, using combinations, the number of ways of selecting 1 stone from 15 stones = 15C1 = 15!/{1! (15 - 1)! } = 15!/1!14! = 15.
For the symbol:
Options available, n = 30.
Options to select, r = 1.
Thus, using combinations, the number of ways of selecting 1 symbol from 30 symbols = 30C1 = 30!/{1! (30 - 1)! } = 30!/1!29! = 30.
The total number of rings available is the product of the three.
Thus, the total number of rings available for selection = 3*15*30 = 1350.
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