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.
questions 49 and 50
![again at 8 P.M. Let s(f) be the distance between Linda and
She did not return to her easy chair until she sat down
62. Last night at 6 P.M., Linda got up from her blue e
61. The cost of manufacturing a container for frozen orange
inches tall. Use Theorem 3.3 to quickly show that he is
height of the container in inches. Your boss claims that
the containers will be cheapest to make if they are 4
juice is C(h) =h2 -7.4h + 13.7 cents, where h is the
42. J
x2 - 4x
[a, b] = [0, 4]
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44. flx) =
x2 – 4x + 3'
T 37
45. f(x) = cosx, [a, b] =
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2' 2
46. f(x) = sin 2x, [a, b] = [0, 27]
47. f(x) = e*(x² – 2x), [a, b] = [0, 2]
48. f2) = In ]x² – 1], [a, b] = [-v2, /2]
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For each graph of f in Exercises 49-52, explain whyf satisfies
the hypotheses of the Mean Value Theorem on the given in-
terval [a, b] and approximate any values ce (a, b) that satisfy
the conclusion of the Mean Value Theorem.
Determine
satisfies the
given interv
gebra to fine
conclusion d
49.
[a, b] = [0, 2]
50.
[a, b] = [-1, 3]
53. f(x) = a
4
54. f(x) = x
55. f(x) = -
56. f(x) = (x
57. f(x) = In(
58. f(x) = 2*,
3
7+
6.
2
4
3-
2+
59. f(x) = sin.
1+
3 -2 -1
60. f(x) = tanx
1
3.
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Applications
necessari
way? Wha
(b) Use Rolle
between 6
respect to
on the grap
wrong.
63. It took Alina ha
is 20 miles from
chair.
easy
(a) Use the Mea
point during
exactly 40 mi
her easyeb
y last night.
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