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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 141 Page 644

Practice makes perfect
a To evaluate the given permutation, we will use the corresponding formula.
_n P_r = n!/(n-r)! We are given that n= 10 and r= 8. Let's substitute these values into the formula and simplify.
_n P_r = n!/(n-r)!
SubstituteII

n= 10, r= 8

_(10) P_8 = 10!/( 10- 8)!
SubTerm

Subtract term

_(10) P_8 = 10!/8!
Next, let's compute the value of _(10) P_8 using the permutation function on our graphing calculator. First we enter the value of n, which is 10 in our case.

Next, push the MATH button, scroll to PRB, and choose the second option. Having chosen _nP_r, we must also enter the value of r, which is 8.

b To evaluate the given combination, we will use the corresponding formula.
_n C_r = n!/(n-r)! r! We are given that n= 10 and r= 8. Let's substitute these values into the formula.
_n C_r = n!/(n-r)! r!
SubstituteII

n= 10, r= 8

_(10) C_8 = 10!/( 10- 8)! 8!
SubTerm

Subtract term

_(10) C_8 = 10!/2! 8!
To calculate this, we can use the graphing calculator's combination function. First we enter the value of n. In our case, it is 10.

Next, push the MATH button, scroll to PRB, and choose the third option. Having chosen _nC_r, you must finish by entering the 8 for r.

c To evaluate the given combination, we will use the corresponding formula.
_n C_r = n!/(n-r)! r! We are given that n= 6 and r= 1. Let's substitute these values into the formula.
_n C_r = n!/(n-r)! r!
SubstituteII

n= 6, r= 1

_6 C_1 = 6!/( 6- 1)! 1!
SubTerm

Subtract term

_6 C_1 = 6!/5! 1!
To calculate this, we can use the graphing calculator's combination function. First we enter the value of n. In our case, it is 6.

Next, push the MATH button, scroll to PRB, and choose the third option. Having chosen _nC_r, you must finish by entering the 1 for r.

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