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Need deduction to help

  1. Sep 5, 2011 #1
    I just meet some easy problem like this,
    Does a monkey have a better chance of rearranging
    I I I L L N O S to spell I L L I N O I S
    E E E E N N S S T to spell T E N N E S S E E ?

    there are 3"I",2"L",1"N",1"O",1"S".
    So P(Illinois)= 8!/(3!*2!*1!*1!*1!)
    My question is that why the answer of ( 8 )*( 5 )*( 3 )*( 2 )*( 1 )
    ////////////////////////////////////////////( 3 )//( 2)//( 1 )//( 1 )/( 1 )

    is exactly 2 times larger than the former one?

    (3)means selecting 3 out of 8
    Last edited: Sep 5, 2011
  2. jcsd
  3. Sep 6, 2011 #2


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    Science Advisor

    What "former one" are you talking about?
    [tex]\frac{8!}{3! 2!}= \frac{8(7)(6)(5)(4)(3!)}{3! 2!}[/tex]
    and we can cancel the "3!" in numerator and denominator. That leaves
    [tex]\frac{8(7)(6)(5)(4)}{2}= 3360[/tex]

    If you are saying that the "answer" (to what question) is
    [tex]\frac{8(5)(3)(2)(1)}{3(2)}= 8(5)= 40[/tex]
    neither is twice the other.

    But what does that have to do with this question?
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