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Math Help - P&C qns: Please help me understand

  1. #1
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    P&C qns: Please help me understand

    1. Three numbers are chosen from 1,2,3,4,5,6,7,8,9. Find the number of arrangements in which the smallest chosen numbers is odd.
    Ans (Highlight to find out) : 300

    2. Find the number of ways in which 10 people can be divided into
    (a) 3 groups consisting of of 2,3, and 5 people
    (b) 2 groups consisting of 3 people each and a group of 4 people
    (c) 5 groups of 2 people each
    Ans: (a)2520 (b)2100 (c)945

    Thanks
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  2. #2
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    Quote Originally Posted by irake View Post
    1. Three numbers are chosen from 1,2,3,4,5,6,7,8,9. Find the number of arrangements in which the smallest chosen numbers is odd.
    Ans (Highlight to find out) : 300

    Mr F says: Number of arrangements with:

    (1 and two other numbers) + (3 and two other numbers greater than 3) + (5 and two other numbers greater than 5) + (7 and two other numbers greater than 7) = 3[(1)(8)(7) + (1)(6)(5) + (1)(4)(3) + (1)(2)(1)] = 3(100) = 300.


    2. Find the number of ways in which 10 people can be divided into
    (a) 3 groups consisting of of 2,3, and 5 people

    Mr F says: {10 \choose 2} \, {8 \choose 3} \, {5 \choose 5} = .......

    (b) 2 groups consisting of 3 people each and a group of 4 people

    Mr F says: \frac{{10 \choose 3} \, {7 \choose 3} \, {4 \choose 4}}{2!} = .......

    (c) 5 groups of 2 people each
    Ans: (a)2520 (b)2100 (c)945

    Mr F says: \frac{{10 \choose 2} \, {8 \choose 2} \, {6 \choose 2} \, {4 \choose 2} \, {2 \choose 2}}{5!} = .......


    Thanks
    But why hide the answers ......?
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  3. #3
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    Ah, I was thinking that maybe you would like to do it yourself first before looking at the answer =\

    I guess my logic was a bit warped, for the first qns, I tried:
    (All odd) + (1 odd 2 even) + (2 odd 1 even)=
    (All odd) + ((odd n0 is 1) + (odd no is 3)+...+(odd no is 7)) + ((smaller odd no is 1)....)
    That's where I got messed up. The second question I was wondering if it was permutations or combi, and got even more messy
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  4. #4
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    Quote Originally Posted by irake View Post
    Ah, I was thinking that maybe you would like to do it yourself first before looking at the answer =\

    I guess my logic was a bit warped, for the first qns, I tried:
    (All odd) + (1 odd 2 even) + (2 odd 1 even)=
    (All odd) + ((odd n0 is 1) + (odd no is 3)+...+(odd no is 7)) + ((smaller odd no is 1)....)
    That's where I got messed up. The second question I was wondering if it was permutations or combi, and got even more messy
    Well, I hope it's all blue sky now
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