Data management

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1)SOLVE:
a) 2nP3 = 2(nP4)
b)6(n+1P2) = 3nP2

2) If (nC12 = (nC8), find (nC17) and (22Cn)

3)simplify.
a) n(squared) (n-2)! - n(n-2)! / n!
b) (nC2) - (nCn-2)

4)If nPr - 506 and (nCr_ = 253, find n and r.

5) If (28C2r)/(24C2r-4) = 225/11, find r.

  • Data management -

    a)
    P(2n,3)=2P(n,4)
    =>
    2n(2n-1)(2n-2)=2n(n-1)(n-2)(n-3)
    cancel 2n to get
    (2n-1)(2n-2)=(n-1)(n-2)(n-3)
    This kind of equation can be readily solved by trial and error, since they both increase monotonically at different rates.
    In this case, n=1 (which is rejected) or n=8.

    try (b) and (2)similarly to (a) above.

    3(a) simplifies well, assuming you have left out the critical square brackets:
    [n²(n-2)!-n(n-2)!]/n!
    (n-2)![n²-n]/n!
    =(n-2)!n[n-1]/n!
    =n!/n!
    =1

    Give a try to 3b.

    4.
    What it is saying is that
    P(n,r)=2C(n,r)
    =>
    n!/(n-r)! = 2*n!/((n-r)!r!)
    Cancel the n! and (n-r)! to get
    1=2/r!
    => r!=2 => r=2
    After that, you only have to check by trial and error C(n,2)=253.

    Give (5) a try.

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