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Combinations

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a brief summary of what my pre-calculus class did on Nov. 29, 2007.

a brief summary of what my pre-calculus class did on Nov. 29, 2007.

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  • 1. Combinations The quot;Choosequot; Formula
  • 2. Hello there! I'm Mary Ann, and I will be your scribe for today.  We started off with a few circle permutation questions as a  warm­up. It was quite simple in the beginning, but, little did we  know what Mr. K had in store for our class today.  It was called COMBINATIONS. Defenition: An arrangement of objects where order does not  matter. (The opposite of a permutation; where order does matter.)
  • 3.      n! This is known as the quot;Choosequot;  = nCr Formula:         formula. (n ­ r)!r! n is the number of objects to choose from. r is the number of objects to be arranged. Example: You have 49 numbers in the 6/49 lottery to  choose from and want to choose 6 numbers for your ticket.  you will then have..       49!      49! 49C6  =  = 13 983 816  = (49 ­ 6)!6!   (43)!6! ways to make your ticket.
  • 4. Example: In how many ways can 8 books be arranged on a shelf, if  3 particular books must be together?       These three books have to be together at all  times. But within these three books, they can  also be arranged in 3! ways.  The same goes with the six books; 6!  ways. (3!)(6!) (6)(720) 4320 ways to arrange the books.
  • 5. Example: How many differnt necklaces of 12 beads can each be  made from 18 beads of different colours? In this question, you are to choose 12 beads from 18 beads.  ∴  18C12 Step 2: Step 1:        18! This side takes care  The  (12 ­ 1)! of the circular  quot;Choosequot;  (18­12)!12!      2 permutation idea,  Formula    18! 11! since the necklace  (6)!12!  2 is a circle and can  be flipped over. 18 564 19 958 400       (18 564)(19 958 400)
  • 6. In the afternoon class, while Mr. K had to run out for a short  while, we had a quiz. (Refer to the post below to look at the  slides where members of our class wrote down the  solutions). The solutions are pretty straight forward, so I  don't think I have to make any clarifications on it. If their are  any questions though, please comment on this post and I, or  someone else who can explain it, will be glad to help. :­) The next scribe is  ­ ­ !! Ecko Montana !! ­ ­

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