Counting, Permutation and Combination

When you toss a coin, how many possible outcome do you have?

• 1

• 2

• 3

• 4

Think of letters  $ABC$ , how many possible ways to rearrange this three letters if each letter can only be used once? (So no AAA or BBB) 

• 3

• 6

• 9

• 12

Think of letters  $AB$  , how many different ways to rearrange these two letters if each letter is reusable? (So allow AA or BB)

• 2

• 4

• 6

• 8

Think of letters  $ABC$ , how many different ways to rearrange these 3 letters if each letter is reusable? (So allow AAA or BBB or CCC)

• 9

• 27

• 81

• 243

So, now think of letters  $T\ H\ I\ N\ K$ , how do we find how many different ways to rearrange those letters if each letter can only be used once? 

•  $5\times4\times3\times2\times1$  

•  $5\times5\times5\times5\times5$  

•  $5\times5\times4\times4\times3$  

•  $1\times2\times3\times4\times5\times6$  

Think of letters  $A\ M\ O\ N\ G\ U\ S$ , how many different ways to rearrange these letters if each letter is reusable?

•  $7\times6\times5\times4\times3\times2\times1$  

•  $7\times7\times7\times7\times7\times7\times7$  

•  $7\times7\times6\times6\times5\times5$  

•  $5\times5\times6\times6\times7\times7\times7$  

Now get your scientific calculator. Can you find ! symbol?

• YES!

• Absolutely!

• I don't have any other option...

So, now let's find out what is the value of  $5!=$ 

• 660

• 480

• 360

• 120

Once again, what is the value of  $6!-3!=$ 

• 914

• 814

• 714

• 614

Is  $5!$ the same with  $\left(5\times4\times3\times2\times1\right)$  ?

• YES

• NO

• Who cares? That 5 looks sus