ns 4
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
![KFUPM – PREP MATH PROGRAM – MATH002 – TERM 203
12.2 & 12.3 Recitation Exercises
1. Find the center, the vertices, foci, and eccentricity of the ellipse given by the
equation
a) 3x2 + 2y2 – 6x + 12y
= -15
b) 3y2 + 2x2 – 6y + 12x = -15
2.
a) Find the equation of the ellipse that has vertices at (3,8) and (3, -2), and
foci at (3,6) and (3,0).
b) Find the equation in standard form, of the ellipse with foci at (-1,2) and
(3,2) that passes through the point (3,5).
(x+1)2
(y-2)2
3. Find the points of intersection of the ellipse
= 1, and the
16
hyperbola
(x+1)²
(y-2)2
= 1:
16
a)
By solving the system of nonlinear equations.
b) By graphing.
4. Find the equation in standard form of the hyperbola with vertices (-1,0) and
V5
(-1,–4), and eccentricity e =
2'
5. Write the following equations in standard form and identify the corresponding
conics
a)
x² – 4x + y2 + 2y + 2 = 0.
b)
2x2 – 8x – 2y? – 4y = 0.
c)
27x2 + 36y2 + 18x + 36y – 96 = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faee2279c-3ded-4856-af66-07025f1971fd%2F52ddbff4-1826-44df-a266-e760675d0b8b%2Fbtno1o6_processed.jpeg&w=3840&q=75)
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