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

1. ## 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.

2. 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.

3. 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.