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Core Connections Geometry, 2013
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Core Connections Geometry, 2013 View details
3. Section 10.3
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Exercise 144 Page 645

Practice makes perfect
a We want to evaluate the given expression given that f(n) = n!. To do so, let's first recall the definition of a factorial
n! = n(n-1) â‹Ż (2)(1) Let's use this definition to evaluate the expression.
f(5)/f(3)
Rewrite

Rewrite f(n) as n!

5!/3!

Write as a product

5(4)(3)(2)(1)/3(2)(1)
â–Ľ
Simplify
ReduceFrac

a/b=.a /3(2)./.b /3(2).

dfrac 5(4) 1
DivByOne

a/1=a

5(4)
Multiply

Multiply

20
b We want to evaluate the given expression given that f(n) = n!. To do so, let's first recall the definition of a factorial
n! = n(n-1) â‹Ż (2)(1) Let's use this definition to evaluate the expression.
f(6)/f(4)
Rewrite

Rewrite f(n) as n!

6!/4!

Write as a product

6(5)(4)(3)(2)(1)/4(3)(2)(1)
â–Ľ
Simplify
ReduceFrac

a/b=.a / 4(3)(2)(1) ./.b / 4(3)(2)(1) .

6(5)/1
DivByOne

a/1=a

6(5)
Multiply

Multiply

30
c We want to evaluate the given expression given that f(n) = n!. To do so, let's first recall the definition of a factorial
n! = n(n-1) â‹Ż (2)(1) Let's use this definition to evaluate the expression.
f(9)/f(7)f(2)
Rewrite

Rewrite f(n) as n!

9!/7!2!

Write as a product

9(8)(7)(6)(5)(4)(3)(2)(1)/7(6)(5)(4)(3)(2)(1)(2)(1)
â–Ľ
Simplify
ReduceFrac

a/b=.a /7(6)(5)(4)(3)(2)(1)./.b /7(6)(5)(4)(3)(2)(1).

9(8)/(2)(1)c
Multiply

Multiply

72/2
CalcQuot

Calculate quotient

36
Subchapter links expand_more
arrow_right 10.3.1 The Fundamental Principle of Counting p.631-633
114
115
116
117
118
The Fundamental Principle of Counting 119 (Page 633)
120
arrow_right 10.3.2 Permutations p.638-640
127
128
129
130
Permutations 131 (Page 639)
Permutations 132 (Page 640)
133
arrow_right 10.3.3 Combinations p.643-645
139
140
Combinations 141 (Page 644)
142
Combinations 143 (Page 644)
Combinations 144 (Page 645)
Combinations 145 (Page 645)
arrow_right 10.3.4 Categorizing Counting Problems p.649-650
153
154
Categorizing Counting Problems 155 (Page 649)
Categorizing Counting Problems 156 (Page 649)
157
158
159
arrow_right 10.3.5 Some Challenging Probability Problems p.658-660
173
174
175
Some Challenging Probability Problems 176 (Page 659)
177
Some Challenging Probability Problems 178 (Page 659)
179
180
181
182
183
184