Question 595250: Toss a penny, nickel, dime and quarter together. How many heads/tails arrangements are possible? Of those, how many have two heads and two tails?
My attempts:
(2C1)*(2C1)*(2C1)*(2C1)=16 possible combinations
How can I find out how many combinations have 2 head and 2 tails? Am I on the right track?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! You are correct. There are 16 possible outcomes.
Of these 16 outcomes, only the following have two heads and two tails
HHTT
HTHT
HTTH
THHT
THTH
TTHH
So there are 6 combinations that have 2 heads and two tails.
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Another way to calculate the above is to notice that there is only way to get all heads HHHH and only one way to get all tails TTTT. So we can subtract these two cases off
We're left with 16 - 2 = 14 cases
There are 4 ways to have exactly one head (one for each slot). They are: HTTT, THTT, TTHT, TTTH
Likewise, there are 4 ways to have exactly one tail, and they are: THHH, HTHH, HHTH, HHHT
So there are now 14 - 4 - 4 = 6 cases left
But the only possible outcome is to have 2 heads and 2 tails. This is because having 3 heads leads to one tail or having 3 tails leads to one head.
So we're led to the same answer of 6.
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