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

**sajjad002** · May 28th 2009, 09:42 PM

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.

**Swlabr** · May 28th 2009, 10:50 PM

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.

**HallsofIvy** · May 29th 2009, 09:32 AM

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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