Apparently, we use "Permutation" when order doesn't matter. In that way, only possible outcomes can be calculated.
P (n, r) = n! ( (n - r)!
Unlike, We use "Combination" when order does matter. Combination gives us all possible values.
C (n, r) = n! / (n - r)! r!
Hope this helps!
Answer:
c) parabola and circle: 0, 1, 2, 3, 4 times
d) parabola and hyperbola: 1, 2, 3 times
Step-by-step explanation:
c. A parabola can miss a circle, be tangent to it in 1 or 2 places, intersect it 2 places and be tangent at a 3rd, or intersect in 4 places.
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d. A parabola must intersect a hyperbola in at least one place, but cannot intersect in more than 3 places. If the parabola is tangent to the hyperbola, the number of intersections will be 2.
If the parabola or the hyperbola are "off-axis", then the number of intersections may be 0 or 4 as well. Those cases seem to be excluded in this problem statement.
In order to compare the fractions, we need to convert them into decimal form,
1/8 = 0.125
3/20 = 0.15
As 0.15 > 0.125
In short, Your Answer would be 3/20 > 1/8
Hope this helps!