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Math Help - A club consists of four memebers.How many sample points are in the sample space when

  1. #1
    Newbie sajjad002's Avatar
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    A club consists of four memebers.How many sample points are in the sample space when

    Q1 . A club consists of four memebers.How many sample points are in the sample space when three officers; president, secretary and treasurer, are to be chosen?


    Q2.
    Use mathematical induction to prove that for all integers n≥1,
    5^n-2^n is divisible by 3.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by sajjad002;322873[FONT=Times New Roman
    [/FONT]]Q2.
    Use mathematical induction to prove that for all integers n≥1,
    5^n-2^n is divisible by 3.

    For question two, your base case is n=1. Clearly this holds.

    So assume the result works for n: 5^n-2^n = 3a, a \in \mathbb{N}. Then, we want to show that 5^{n+1}-2^{n+1} = 3b, b \in \mathbb{N}.

    Hint: Substitute 5^n-2^n = 3a into 5^{n+1}-2^{n+1} only once.
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  3. #3
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    For Question 1, there are 4 possible choices for president, leaving 3 people that could be chosen secretary, then 2 that could be chosen treasurer. That is a total of 4(3)(2)= 24 choices.
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