MOKSH wrote:
You are given an unlimited number of circles each of which having radii either 2 or 4. You must place the circles side-by-side so that they only touch at one point. If exactly two of the smaller circles are used, in how many different ways may the circles be placed next to one another so that the centers of the circles are all on the same straight line and so that the sum of the lengths of the diameters of the circles is 32?
A. four
B. six
C. eight
D. ten
E. twelve
The the sum of the lengths of the
diameters of two smaller circles is 2*4=8.
Hence, the sum sum of the lengths of the
diameters of larger circles is 32-8=24, which means that there should be 24/8=3 large circles.
So, we have that there should be 2 small circles and 3 large circles.
The number of arrangement is 5!/(3!*2!)=10 (the number of arrangements of 5 objects in a row, where 3 of the objects are identical and the remaining 2 objects are identical as well).
Answer: D.
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