If you throw a coin 6 times how many possible outcomes are there?

Answer 1

Whenever you are trying to figure out the answer to an outcome problem, you just multiply how many sides it has by how many times you are tossing the coin.... 2 x 6 = 12 times.

===================================

Very reasonable. Warm, fuzzy, and intuitively satisfying. But, sadly, wrong.

Every toss of a coin has 2 possible outcomes.

If you write down the results of 6 tosses like: H T T H T H with an 'H' for each heads

and a 'T' for each tails, the number of different patterns you could write down for

six tosses is

2 x 2 x 2 x 2 x 2 x 2 = 64 .

If you don't care about the sequence, and you just want to know how many

different splits of 'heads' vs 'tails' you could get in 6 tosses, then there are seven

different possible outcomes:

-- no heads, 6 tails

-- 1 heads, 5 tails

-- 2 heads, 4 tails

-- 3 heads, 3 tails

-- 4 heads, 2 tails

-- 5 heads, 1 tails

-- 6 heads, no tails