if you toss 4 fair coins, in how many ways can you obtain atleast 2 heads?

Question

Can you please explain I have no idea and im kinda confused

Answer 1

Note that 1! = 1

 

2 heads:

 

(4 choose 2) = 4!/(2!)(2!) = 24/(2*2) = 24/4 = 6

hhtt thht

htht thth

htth tthh

 

3 heads

(4 choose 3) = 4!/(3!*1!) = 24/6 = 4

 

hhht

hhth

hthh

thhh

 

4 heads:

hhhh

 

Total is 6 + 4 + 1 = 11

Answer 2

Let's look a the question this way.

Each coin can land on a heads or a tails

And you have 4 coins.

 

Here are the possibilities.  (Each letter is another coin.)

 

All heads - only 1 way

HHHH

 

One Tail/3 heads - 4 ways

HHHT

HHTH

HTHH

THHH

 

Two Tails/ two heads - 6 ways

HHTT

HTHT

HTTH

TTHH

THHT

THTH

 

3 Tails/1 head - 4 ways

TTTH

TTHT

THTT

HTTT

 

4 Tails - only 1 way

TTTT

 

At least 2 heads means 2 heads or 3 heads or 4 heads

There are 6 ways to get 2 heads, 4 ways to get 3 heads and 1 way to get 4 heads.

This is a total of 6+4+1 = 11 ways to get at least 2 heads.