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Math Question

Discussion in 'DAT Discussions' started by Ferdowsi, May 30, 2008.

  1. Ferdowsi

    2+ Year Member

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    I saw this problem and couldn't figure it out
    so here is the ques:
    from a group of 3 violinists and 4 pianists, a judge must select 2 violinists and 2 pianists to perform at a music recital. How many different combinations of musicians might perform at recital?


    and there is another one close to that:
    from a group of 3 singers and 3 comedians, a show organizer must select 2 singers and 2 comedian to appear one after another in a show. how many different ways can the organizer arrange performers for the show?

    it's so frustrating :(
     
  2. vvvv

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    first one. 2C3 * 2C4 =
    second: 2C3 * 2C3 =
     
  3. Ferdowsi

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    I don't get it..wat's C

    but the answer for the first one is 18
    and the second one is 216
     
  4. vvvv

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    C is combination. because the order in this case is not matter so we use C. formular of C is nCm = m!/n! (m-n)1.
    so 2C3 * 2C4 = 3!/2!*1! * 4!/2! * 2! = 18

    the second one I dont think you give the right answer.
     
  5. Ferdowsi

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    thanks for the formula.but for the second one it is the rite answer...i don't know how
     
  6. vvvv

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    If you think about the second one, it should be lower number than the first one because 4 compare to 3. if you could count them out, you will see the answer is not sounded right
     
  7. Streetwolf

    Streetwolf Ultra Senior Member
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    First off vvvv you do the big number C the little number, so you do (3 C 2) for example (read "three choose two"). That's just been buggin' me a little bit. :p

    First one is asking for the musicians that will perform so it's a combination. You do (3 C 2) for the violinists and (4 C 2) for the pianists. This picks the 2 violinists and the 2 pianists. You get (3 C 2) = 3 and (4 C 2) = 6 so 3*6 = 18.

    Second one is asking for the total number of arrangements. Order MATTERS because the organizer wants the number of ways to arrange a lineup for the show. This is technically a permutation but the easiest way to do it is to use a combination.

    You have three comedians and three singers. You want two of each. First determine the number of ways you can select who performs. You do (3 C 2) and (3 C 2) = 3*3 = 9. So you have 9 different groups of 4 people that you could select, without regard to order. Now you want to place them in order. For any group of 4 people, you can order them in 4! = 24 ways. So you take 9*24 = 216 and that's your answer.
     
  8. vvvv

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    excellent.
     

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