Illustrative Example 4: Illustrative Example 5: Rewrite the following factorials. Evaluate each factorial notation. a. 12! with a factor 9! 12! = 12 x 11 x 10 x 9! a. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720 b. 15! with a factor 13! 15! = 15 x 14 x 13! b. (6 – 2)! = 4! = 4 x 3 x 2 x 1 = 24 c. 10! with a factor 5! 10! = 10 x 9 x 8x 7 x6 x 5! 7! C. 4!+3! 7x6x5x4x3x2x1 5,040 = 168 %3D (4x3x2x1)+3x2×1) 24+6 Learning Task B Directions: Evaluate each Factorial notation. Show your complete solution. 1. 8! 2. (9 + 1)! %3D 3. 6! (5 – 2)! 4. 4! + 5! %3D 5. 8! 6! %3D

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 43E
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Please answer Learning task B And Assessment, number 4 and 5 only

 

 

 

Illustrative Examples 7: Find the unknown variable.
b. Р(п, 3) %3D 990
9P, = 504
Solution:
а.
Solution:
504
Р(п, 3) %3D
990
||
9!
504
n!
990
(9-r)!
362,880
(n-3)!
504
(9-г)!
362,880
n(n-1)(n-2)(n-3)!
(n-3)!
990
(9 — г)!
504
n(n – 1)(n – 2) = 990
(9 – r)!
(9 — г)!
(9 — г)
720 =
6!:
n(n – 1)(n – 2) =
11 x 10 × 9
6 =
n =
11
6 – 9 =
-r
-3%3D
-r
3 =
r
Assessment:
Directions: Apply the formula in finding the number of Permutation of n objects taken r at a time.
Write only the letter of the correct answer.
1.
What is 10P3?
C. 1,200
D. 5,040
В. 720
If P( 8,r ) = 336, which of the following is the value of r?
В. З
If P(n,4) = 11,880, which of the following is the value of n?
В. 10
A. 120
2.
A. 2
С. 4
D. 5
3.
А. 8
%3D
С. 12
D. 14
James has downloaded 15 songs on his cellphone. How many different ways can he play 5 songs?
С. 12,350
4.
В. 5,040
In how many ways can 7 potted pots be arranged in a row?
B. 720
A. 225
D. 360,360
5.
А. 330
С. 2,210
D. 5,040
Transcribed Image Text:Illustrative Examples 7: Find the unknown variable. b. Р(п, 3) %3D 990 9P, = 504 Solution: а. Solution: 504 Р(п, 3) %3D 990 || 9! 504 n! 990 (9-r)! 362,880 (n-3)! 504 (9-г)! 362,880 n(n-1)(n-2)(n-3)! (n-3)! 990 (9 — г)! 504 n(n – 1)(n – 2) = 990 (9 – r)! (9 — г)! (9 — г) 720 = 6!: n(n – 1)(n – 2) = 11 x 10 × 9 6 = n = 11 6 – 9 = -r -3%3D -r 3 = r Assessment: Directions: Apply the formula in finding the number of Permutation of n objects taken r at a time. Write only the letter of the correct answer. 1. What is 10P3? C. 1,200 D. 5,040 В. 720 If P( 8,r ) = 336, which of the following is the value of r? В. З If P(n,4) = 11,880, which of the following is the value of n? В. 10 A. 120 2. A. 2 С. 4 D. 5 3. А. 8 %3D С. 12 D. 14 James has downloaded 15 songs on his cellphone. How many different ways can he play 5 songs? С. 12,350 4. В. 5,040 In how many ways can 7 potted pots be arranged in a row? B. 720 A. 225 D. 360,360 5. А. 330 С. 2,210 D. 5,040
Illustrative Example 4:
Illustrative Example 5:
Rewrite the following factorials.
Evaluate each factorial notation.
a. 12! with a factor 9! 12! = 12 × 11 × 10 × 9!
a. 6! = 6 x 5 × 4 × 3 × 2 × 1 = 720
b. 15! with a factor 13! 15! = 15 × 14 × 13!
b. (6 – 2)! = 4! = 4 × 3 × 2 × 1 = 24
7!
С.
4!+3!
c. 10! with a factor 5! 10! = 10 × 9 × 8 ×7 x6 × 5!
7x6x5x4x3×2×1
5,040
= 168
(4x3×2x1)+3×2×1)
24+6
Learning Task B
Directions: Evaluate each Factorial notation. Show your complete solution.
1. 8!
%3D
2. (9 + 1)!
3. 6! (5 – 2)!
4. 4! + 5!
%3D
5. 8! 6!
Transcribed Image Text:Illustrative Example 4: Illustrative Example 5: Rewrite the following factorials. Evaluate each factorial notation. a. 12! with a factor 9! 12! = 12 × 11 × 10 × 9! a. 6! = 6 x 5 × 4 × 3 × 2 × 1 = 720 b. 15! with a factor 13! 15! = 15 × 14 × 13! b. (6 – 2)! = 4! = 4 × 3 × 2 × 1 = 24 7! С. 4!+3! c. 10! with a factor 5! 10! = 10 × 9 × 8 ×7 x6 × 5! 7x6x5x4x3×2×1 5,040 = 168 (4x3×2x1)+3×2×1) 24+6 Learning Task B Directions: Evaluate each Factorial notation. Show your complete solution. 1. 8! %3D 2. (9 + 1)! 3. 6! (5 – 2)! 4. 4! + 5! %3D 5. 8! 6!
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