Fundamental Counting Principle:
In a series of events, the net possible number of ways all events can executed is the product of the possible number of manners each individual event can be executed.
The Bluman text states this multiplication principle 2.
Factorials:
When n is a positive integer, then
n! = n (n-1) (n-2) ... (3) (2) (1)n! = n (n-1)!A special case is 0!0! = 1
Permutations:
The permutation can be defined as an arrangement of objects without repetition where order is very important.
Permutations utilizing all the objects:
The permutation of n objects, arranged to one group of size n, with no repetition, and order being significant is:
nPn = P(n,n) = n!
Illustration: Find out all the permutations of letters ‘ABC’
ABC ACB BAC BCA CAB CBA
Permutations of some of objects:
The permutation of n objects, arranged in a group of size r, with no repetition, and order being significant is:
nPr = P(n,r) = n!/(n-r)!
Illustration: Find out all the two-letter permutations of letters ‘ABC’
AB AC BA BC CA CB
Shortcut formula for finding a permutation:
Supposing that you begin a n and count down to 1 in your factorials..
P(n,r) = first r factors of n factorial
Distinguishable Permutations:
Many times letters are repeated and all of the permutations are not differentiateable from one other.
Illustration: Find out all the permutations of letters ‘BOB’
To help you differentiate, we will write the second ‘B’ as ‘b’
BOb BbO OBb ObB bBO bOB
If we can write ‘B’ as ‘B’, we get:
BOB BBO OBB OBB BBO BBO
There are actually only three distinguishable permutations here.
BOB BBO OBB
When a word has N letters, k of which are exclusive, and you let n (n1, n2, n3... nk) be the frequency of each of k letters, then the total number of distinguishable permutations is provided by:
N!/(n1! * n2! ... nk!)
Let consider the word "STATISTICS":
Here is the frequency of each letter: S=3, T=3, A=1, I=2, C=1, there are total 10 letters
Permutations = 10!/(3! 3! 1! 2! 1!) = (10*9*8*7*6*5*4*3*2*1)/( 6 * 6 * 1 * 2 * 1) = 50400Combinations:
The combination can be defined as an arrangement of objects with no repetition where order is not significant.
It must be noted that the difference between a combination and permutation is not whether there is repetition or not -- there should not be repetition with either, and when there is repetition, you cannot use the formulas for permutations or combinations. The merely difference in the definition of permutation and a combination is whether order is much important.
The combination of n objects, arranged in a group of size r, with no repetition, and order being significant is:
nCr = C(n,r) = n!/((n-r)! * r!)
The other way to write a combination of n things, r at a time is utilizing the binomial notation: n over r in parentheses devoid of a fraction bar
Illustration: Find out all two-letter combinations of letters ‘ABC’
AB = BA AC = CA BC = CB
The answer is just a three two-letter combinations.
Shortcut formula for determining combination:
Supposing that you begin a n and count down to 1 in your factorials....
C(n,r) = first r factors of n factorial divided by the last r factors of n factorial
Pascal's Triangle:
The combinations are utilized in the binomial expansion theorem from algebra to provide the coefficients of expansion (a+b)^n. They as well form a pattern termed as Pascal's Triangle. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1
Each and every element in the table is the sum of two elements directly above it. Each and every element is as well a combination. The n value is a number of row (start counting at zero) and the r value is an element in the row (start counting at zero). That would make the 20 in next to last row C(6,3) -- it's in the row #6 (that is, 7th row) and position #3 (that is, 4th element).
Symmetry:
Pascal's Triangle describes the symmetric nature of combination. C(n,r) = C(n,n-r)
Illustration: C(10,4) = C(10,6) or C(100,99) = C(100,1)
Shortcut formula for finding a combination:
As combinations are symmetric, when n-r is smaller than r, then switch the combination to its alternative form and then employ the shortcut given above.
C(n,r) = first r factors of n factorial divided by last r factors of n factorialTree Diagrams:
Tree diagrams are a graphical method of listing all possible outcomes. The outcomes are listed in an arranged fashion, therefore listing all the possible outcomes is simpler than just trying to make sure that you have them all listed. It is termed as a tree diagram since of the way it looks.
The first event comes into views on left, and then each sequential event is symbolized as branches off of first event.
The tree diagram to right would illustrate the possible ways of flipping the two coins. The final outcomes are obtained by following each and every branch to its conclusion: They are from top to bottom.
HH HT TH TT
Latest technology based Statistics Online Tutoring Assistance
Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Statistics help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Statistics, project ideas and tutorials. We provide email based Statistics help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Statistics. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Statistics Homework help and assignment help services. They use their experience, as they have solved thousands of the Statistics assignments, which may help you to solve your complex issues of Statistics. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.
the insulating materials are categorized in the following two ways - classification as per to substances and materials, classification as per to temperature.
www.tutorsglobe.com offers stereogenic nitrogen homework help, stereogenic nitrogen assignment help, online tutoring assistance, organic chemistry solutions by online qualified tutor's help.
tutorsglobe.com income assignment help-homework help by online basic economics sense tutors
tutorsglobe.com huntington’s chorea assignment help-homework help by online genetic diseases tutors
Explore the brilliance of best International Economics Assignment Help instantly to secure top grades at budget-friendly prices.
Free AP Biology Study Guide, AP Biology Test Papers, AP Biology Practice papers, AP Biology Test pattern and general information, Find AP Biology exam information and resource, material free at Tutorsglobe.com
tutorsglobe.com gluconeogenesis of glycerol assignment help-homework help by online gluconeogenesis tutors
Phylum Chordata Class Aves-Birds tutorial all along with the key concepts of Adaptations of Class Aves-Birds, Feather, Wings, Uses of Feather, Oxygen Supply and Energy in birds and Migration
tutorsglobe.com programming in java script assignment help-homework help by online computer programming tutors
tutorsglobe.com degradation of phospholipids by enzymes assignment help-homework help by online phospholipids tutors
an mp3 cd is a compact disc (generally a cd-r or cd-rw) which consist of digital audio in the mp3 file format.
Tuned base oscillator tutorial all along with the key concepts of Circuit Action, Tuned Collector Oscillator, Positive Feedback, Hartley Oscillator, Colpitts Oscillator, Clapp Oscillator, Piezoelectric Effect, Q-factor
To make use of immersion water heater, one just fills a bucket of water and puts the immersion rod into the bucket either with an aid such as a clothes hanger or directly.
electromagnetic induction tutorial all along with the key concepts of time - varying magnetic field, induced e.m.f. and currents, statement of faraday's law, lenz's law, fleming's right-hand rule and generators
www.tutorsglobe.com offers Design Fundamentals homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
1930891
Questions Asked
3689
Tutors
1467191
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!