Permutations, combinations and factorial

Question 1

Finish P,20,3)..

Answer 1

> 20! / 171
>

Question 2

How many non-repetitive words of length 4 can you make from the letters {a, b, c, d, e, f}?

Answer 2

As there is 6 letters you do 6! / 4!
>
6 x 5 x 4 x 3 x 2 x 1
4 x 3 x 2 x 1

> > 720 / 24
= 30

Question 3

What is a Permutation?

Answer 3

The number of ways a set can be arranged

Question 4

What is a combination?

Answer 4

When the order doesn’t matter

Question 5

How many binary strings of length 8 contain equal number of 0 and 1?

Hint: the order does not matter so it is a combination

Answer 5

• 8 positions
  ** four 1’s

So…

C(8,4) =
> 8! / 4!(4)! =
» 8x7x6x5 / 4x3x2x1 =
»> 70