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Probability Question - Sequences?

  • 06-12-2014 2:23pm
    #1
    TheSetMiner
    Registered Users, Registered Users 2 Posts: 225 ✭✭


    A ternary string is a sequence of 0s, 1s, and 2s. How many ternary strings of
    length 15 are there?

    Answer:
    3^15
    How many of those strings contain exactly seven 0s, five
    1s, and three 2s?

    Answer:
    I am pretty unsure here. Does this question depend on the first part in any way? Logically it feels like 15c7 . 8c5 . 3c3 is the correct answer?
    But having done a bit of googling I have seen other approaches which made no sense to me. Can anyone clarify if I am right?

    How many ternary strings of length 15 have even weight, i.e.,
    contain an even number of 1s?

    Answer:
    15c2 . 3^13 + 15c4 . 3^11 + 15 c 6 . 3 ^ 9 + ... + 15c14 . 3^1

    Is this correct?

    If anyone can offer a second opinion on my solutions, that would be very helpful, thanks in advance!


Comments

  • #2
    MathsManiac
    Registered Users, Registered Users 2 Posts: 1,595 ✭✭✭MathsManiac


    Your first two answers are correct.

    In the third one, you need to bear in mind that, after you select the position for the 1s, the remaining entries can't be 1, so your powers of 3 should be powers of 2. Also, you've omitted the possibility that there be no 1s in the string: (15C0).2^15 = 2^15.


  • #3
    TheSetMiner
    Registered Users, Registered Users 2 Posts: 225 ✭✭TheSetMiner


    MathsManiac wrote: »
    Your first two answers are correct.

    In the third one, you need to bear in mind that, after you select the position for the 1s, the remaining entries can't be 1, so your powers of 3 should be powers of 2. Also, you've omitted the possibility that there be no 1s in the string: (15C0).2^15 = 2^15.

    powers of 2 makes sense alright and I completely forgot zero was en even number! Much appreciated!


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