Kevin Flores - M5 Ordering Worksheet
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National Louis University *
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Course
101
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
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4
Uploaded by kf394534
MTH 101
Module 5 Ordering Worksheet
1.
Johnny has 3 types of spring jackets, 2 types of winter jackets, and 7 types of
running jackets. How many total types of jackets does Johnny own?
3+2+7=12
Johnny owns 12 total types of jackets.
The Fundamental Counting Principle
… 2.
A gift wrapping store has 8 shapes of boxes, 14 types of wrapping paper, and
12 different bows. How many different gift-wrapping options are available at this store? 8*14*12 = 1344 different gift-wrapping options.
Definition of factorial
– n!
3.
Simplify: 7! 7! = 7*6*5*4*3*2*1 = 5,040
Permutation
= ordering of objects 4.
Four friends go to the movies. How many distinct ways can they sit in a row? 4!= 4*3*3*2*1 = 24
They can sit in 24 distinct ways. Formula – n!
5.
You are creating a 4 digit password using only the 26 letters from the alphabet. How many unique passwords could you create (assuming the password does not need to spell a real word!)? C(26,4)= 26!/4!(26-4)
C(26,4)=26*25*24*23*22/4*3*2*1(22)
C(26,4)= 7,893,600/24(22)
MTH 101
C(26,4)= 7,893,600/528
C(26,4)= 14,950
What are non-distinct
objects?
This mean that the objects cant be distinguished.
6.
Landscape workers are re-developing a popular street. They are planting 12 maple trees, 6 oak trees, and 6 poplar trees. How many distinct ways can they plant these trees? 24!/12!6!6! = 24*23*22*21*20*19*18*17*16*15*14*13 = 1295253
6*5*4*3*2*1(6*5*4*3*2*1) 720(6*5*4*3*2*1)
= 1799020
90 = there are 249864 distinct ways they can plant trees
720
Combination
= a sequence of outcomes where the order does not matter
Formula – C(n,r)= n!
r!(n-r)!
7.
Two people out of a group of 75 will win tickets to an upcoming concert. How
many different groups of two are possible?
C(75,2)= 75
! = there are 2775 different groups of two.
2!(75-2)!
8.
Barry is hosting a Super Bowl party and offers 7 different kinds of chip dip. If a party goes can choose any number of chip dips for their chips, how many chip dip combinations are possible?
7!= 7*6*5*4*3*2*1= 5040
9.
Probability Terminology
Independent
- if the occurrence of one event does not affect the chances of the occurrence of the other event
.
MTH 101
Dependent - when the outcome of the first event influences the outcome of the second event
.
Trial
- any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space
.
Mutually Exclusive
- two or more events that cannot happen simultaneously
.
Event
- the outcomes of an experiment
Outcome
- a possible result of an experiment or trial.
10.
Stacy has 7 blue pens, 9 black pens, and 4 red pens. What is the probability that a pen picked at random is red? Give your answer as a simplified fraction AND decimal. 1/20= 0.05 11.
A twelve sided die is thrown. What is the probability the number rolled will be a multiple of 5? Write your answer as a simplified fraction AND a decimal rounded to the hundredth place. 1/12=
0.083
12.
There are 30 students in the classroom competing for classroom prizes. Only the first two students whose name is drawn will win a prize. The first student wins 5 bonus points and the second student wins 2 bonus points, both on the upcoming test. If you are one of the 30 students, what is the probability you will win the top prize and your best friend wins the second prize?
Student 30 = me … 30-1 = 29 students left
1/29= 0.034 is the probability 13.
There are 14 men and 16 women at jury selection. What is the probability that exactly 6 men and 6 women are chosen for jury duty? Round your answer to the nearest thousandth.
C(14,6) = 14! = 3003.
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MTH 101
6!(14-6)!
C(16,6) = 16! = 8008. 6!(16-6)!
8008/3003 = 2.667