Question 1193952: an optical shop sells 10 types of plastic frames, 12 types of rimless frames and 9 types of metal frames. each pair of glasses can be matched with normal lens, non reflective lens, or anti scratching, non reflective lens. Molly is going to buy a pair of glasses from the shop how many choices does she have?
Found 3 solutions by Theo, greenestamps, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe it will be 10 * 12 * 9 * 4 = 4320 possible choices.
to understand why, use a much simpler example.
let p = number of different types of plastic frames.
let r = number of different types of rimless frames.
let m = number of different types of metal frames.
let l = number of different types of lenses.
let p = 2 and r = 3 and m = 1 and l = 2
the number of choices would be 2 * 3 * 1 * 2 = 12.
the different types of plastic frames would be p1 and p2.
the different types of rimless frames would be r1 and r1 and r3
the different types of metal frames would be m1
the different types of lenses would be l1 and l2
the choices would be:
p1 m1 r1 l1
p1 m1 r1 l2
p1 m1 r2 l1
p1 m1 r2 l2
p1 m1 r3 l1
p1 m1 r3 l2
p2 m1 r1 l1
p2 m1 r1 l2
p2 m1 r2 l1
p2 m1 r2 l2
p2 m1 r3 l1
p2 m1 r3 l2
that's 12 possible choices.
the concept is valid, so it is applies to the larger numbers to get:
10 * 12 * 9 * 4 = 4320 possible choices.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The other tutor didn't read the problem....
When selecting a pair of glasses, you only choose one frame -- you don't choose one plastic frame, one rimless frame, and one metal frame.
Also, with the punctuation used in the statement of the problem, there are only three types of lenses instead of four:
normal
non-reflective
anti-scratching, non-reflective
So there are 10+12+9 = 31 frames to choose from, and 3 types of lenses to choose from.
ANSWER: 31*3 = 93 different possible choices
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Thanks to tutor @ikleyn for pointing out my silly computational error....
Answer by ikleyn(52781)  (Show Source):
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