Results 1 to 9 of 9

Thread: Hard perms and combs question

  1. #1
    Cadet JustRandomThings's Avatar
    Join Date
    Jun 2016
    HSC
    2018
    Gender
    Male
    Posts
    50
    Rep Power
    1

    Hard perms and combs question

    Sorry for bombarding with questions but I really don't know how to approach this question

    Teach me the logic behind these questions pls Thanks in advance

    From the letters of the word WOOLLOOMOOLOO four letters are hosen are chosen at random
    Find the number of ways that
    (i) No O’s are chosen
    (ii) only O’s are chosen
    (iii) The three L’s are chosen
    (iv) no more than one Ois chosen
    (v) at least one L is chosen
    (vi) only O’s and L’s are chosen if it is known at least two L’s have been chosen
    Prelimss 2017


    Asian 5 (Ayyyy farming school)

    HSC 2018

    4U maths
    3U english
    Chemistry
    Physics

  2. #2
    Stars and Bars pikachu975's Avatar
    Join Date
    May 2015
    HSC
    2017
    Gender
    Male
    Location
    NSW
    Posts
    1,433
    Rep Power
    2

    Re: Hard perms and combs question

    Quote Originally Posted by JustRandomThings View Post
    Sorry for bombarding with questions but I really don't know how to approach this question

    Teach me the logic behind these questions pls Thanks in advance

    From the letters of the word WOOLLOOMOOLOO four letters are hosen are chosen at random
    Find the number of ways that
    (i) No O’s are chosen
    (ii) only O’s are chosen
    (iii) The three L’s are chosen
    (iv) no more than one Ois chosen
    (v) at least one L is chosen
    (vi) only O’s and L’s are chosen if it is known at least two L’s have been chosen
    i) No O's so there's 5 letters and we must pick 4 - 5C4

    ii) 8 O's so 8C4

    iii) We pick the 3 L's through 3C3 then 1 letter from the others so 10C1, 3C3 x 10C1

    iv) Pick one O first, so 8C1, now pick the other 3 letters from the non-O's so 5C3 x 8C1

    v) For this we can do complementary event so total ways minus ways to pick zero L's. Total is just 13C4 and the ways to pick no L's is 10C4 as there are 3 L's so we can pick from 10 letters only. Therefore 13C4 - 10C4

    vi) Two L's are chosen at least so there's 2 or 3. For 2 it's 8C2 to pick the remaining O's. For 3 it's just 8C1 to pick the 1 O. Add these to get 8C2 + 8C1

    Correct me if I'm wrong, hope this helped.
    2016 HSC (Accelerated)
    // 2 Unit Maths // Studies of Religion 1 //

    2017 HSC
    // Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //

  3. #3
    Cadet JustRandomThings's Avatar
    Join Date
    Jun 2016
    HSC
    2018
    Gender
    Male
    Posts
    50
    Rep Power
    1

    Re: Hard perms and combs question

    Quote Originally Posted by pikachu975 View Post
    i) No O's so there's 5 letters and we must pick 4 - 5C4

    ii) 8 O's so 8C4

    iii) We pick the 3 L's through 3C3 then 1 letter from the others so 10C1, 3C3 x 10C1

    iv) Pick one O first, so 8C1, now pick the other 3 letters from the non-O's so 5C3 x 8C1

    v) For this we can do complementary event so total ways minus ways to pick zero L's. Total is just 13C4 and the ways to pick no L's is 10C4 as there are 3 L's so we can pick from 10 letters only. Therefore 13C4 - 10C4

    vi) Two L's are chosen at least so there's 2 or 3. For 2 it's 8C2 to pick the remaining O's. For 3 it's just 8C1 to pick the 1 O. Add these to get 8C2 + 8C1

    Correct me if I'm wrong, hope this helped.
    For question iv) wouldn't you also include a case with no zeros?
    Prelimss 2017


    Asian 5 (Ayyyy farming school)

    HSC 2018

    4U maths
    3U english
    Chemistry
    Physics

  4. #4
    Stars and Bars pikachu975's Avatar
    Join Date
    May 2015
    HSC
    2017
    Gender
    Male
    Location
    NSW
    Posts
    1,433
    Rep Power
    2

    Re: Hard perms and combs question

    Quote Originally Posted by JustRandomThings View Post
    For question iv) wouldn't you also include a case with no zeros?
    There are only 3 L's and it says only O's and L's are chosen so there must be an O.
    2016 HSC (Accelerated)
    // 2 Unit Maths // Studies of Religion 1 //

    2017 HSC
    // Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //

  5. #5
    Junior Member BenHowe's Avatar
    Join Date
    Aug 2015
    HSC
    2016
    Gender
    Male
    Location
    Sydney
    Posts
    203
    Rep Power
    2

    Re: Hard perms and combs question

    You've missed some cases and arrangements. These letter ones are generally easier to do with perms I find
    Last edited by BenHowe; 10 Aug 2017 at 10:34 PM.
    1st Year BAppFinBActStud @ MQ

  6. #6
    Stars and Bars pikachu975's Avatar
    Join Date
    May 2015
    HSC
    2017
    Gender
    Male
    Location
    NSW
    Posts
    1,433
    Rep Power
    2

    Re: Hard perms and combs question

    Quote Originally Posted by BenHowe View Post
    You've missed some cases and arrangements. These letter ones are generally easier to do with perms I find
    Yeah but idk about the wording since it just says the letters are chosen
    2016 HSC (Accelerated)
    // 2 Unit Maths // Studies of Religion 1 //

    2017 HSC
    // Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //

  7. #7
    Cadet JustRandomThings's Avatar
    Join Date
    Jun 2016
    HSC
    2018
    Gender
    Male
    Posts
    50
    Rep Power
    1

    Re: Hard perms and combs question

    For question 1, since you can only choose from 1 w , 1 M, 3 L and you need to choose 4, wouldn't there be only 3 cases. MLLL, WLLL, MWLL. The order is not important since the question states how many ways of choosing which implicates combination
    Prelimss 2017


    Asian 5 (Ayyyy farming school)

    HSC 2018

    4U maths
    3U english
    Chemistry
    Physics

  8. #8
    Junior Member BenHowe's Avatar
    Join Date
    Aug 2015
    HSC
    2016
    Gender
    Male
    Location
    Sydney
    Posts
    203
    Rep Power
    2

    Re: Hard perms and combs question

    well since it says chosen we are only interested in the total combinations not the arrangements of the words
    1st Year BAppFinBActStud @ MQ

  9. #9
    Stars and Bars pikachu975's Avatar
    Join Date
    May 2015
    HSC
    2017
    Gender
    Male
    Location
    NSW
    Posts
    1,433
    Rep Power
    2

    Re: Hard perms and combs question

    Quote Originally Posted by JustRandomThings View Post
    For question 1, since you can only choose from 1 w , 1 M, 3 L and you need to choose 4, wouldn't there be only 3 cases. MLLL, WLLL, MWLL. The order is not important since the question states how many ways of choosing which implicates combination
    But there's still 5 ways u can pick the letters because the L's are different. You could pick WML1L2, WML1L3, WML2L3, WL1L2L3, ML1L2L3 which is 5C4 i.e. 5 ways to pick.
    2016 HSC (Accelerated)
    // 2 Unit Maths // Studies of Religion 1 //

    2017 HSC
    // Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •