1 / 16

COMBINATIONS AND PERMUTATIONS

COMBINATIONS AND PERMUTATIONS. REVISION PROBABILITY. A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed three times, what is the probability of getting two tails and one head?. T hree Sigma Rule.

crwys
Download Presentation

COMBINATIONS AND PERMUTATIONS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. COMBINATIONS AND PERMUTATIONS

  2. REVISION PROBABILITY A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed three times, what is the probability of getting two tails and one head?

  3. Three Sigma Rule Three-sigma rule, or empirical rule states that for a normal distribution, nearly all values lie within 3 standard deviations of the mean.

  4. EXAMPLE The scores for all students taking SAT (Scholastic Aptitude Test) in 2012 had a mean of 490 and a Standard Deviation of 100: • What percentage of students scored between 390 and 590 on this SAT test ? • One student scored 795 on this test. How did this student do compared to the rest of the scores? • NUST only admits students who are among the highest 16% of the students in this test. What score would a student need to qualify for admission to the NUST?

  5. Permutation • A permutation is an arrangement of all or part of a set of objects. • Number of permutations of n objects is n! • Number of permutations of n distinct objects taken r at a time is nPr = n! (n – r)! • Number of permutations of n objects arranged is a circle is (n-1)!

  6. Permutations • The number of distinct permutations of n things of which n1 are of one kind, n2 of a second kind, …, nk of kth kind is n! n1! n2! n3! … nk!

  7. Combinations • The number of combinations of n distinct objects taken r at a time is With Replacement : Without Replacement : n + r– 1 Cr = (n + r – 1)! r! (n – 1)! nCr = n! r! (n – r)!

  8. Problem 1 A showroom has 12 cars. The showroom owner wishes to select 5 of these to display at a Car Show. How many different ways can a group of 5 be selected ?

  9. Problem 2 List following of vowel letters taken 2 at a time: • All Permutations • All Combinations without repetitions • All Combinations with repetitions

  10. Problem 3 In how many ways can we assign 8 workers to 8 jobs (one worker to each job and conversely) ?

  11. Problem 7 2 items are defective out of a lot of 10 items: • Find the number of different samples of 4 • Find the number of different samples of 4 containing: (1) No Defectives (2) 1 Defective (3) 2 Defectives

  12. Problem 9 A box contains 2 blue, 3 green, 4 red balls. We draw 1 ball at random and put it aside. Then, we draw next ball and so on. Find the probability of drawing, at first, the 2 blue balls, then 3 green ones and finally the red ones ?

  13. Problem 11 Determine the number of different bridge hands (A Bridge Hand consists of 13 Cards selected from a full deck of 52 cards)

  14. Problem 13 If 3 suspects who committed a burglary and 6 innocent persons are lined up. What is the probability that a witness who is not sure and has to pick three persons will pick 3 suspects by chance? That person picks 3 innocent persons by chance?

  15. Problem 15 How many different license plates showing 5 symbols, namely 2 letters followed by 3 digits, could be made ?

More Related