Here's a problem I'm working on myself.....If you look at six consecutive spins of a roulette wheel, how many combinations of red and black are possible? I.E. BRRBRB, BBBBBR, BBRRRB......ETC.....Hi Bob,
This is the same number as the number of Heads-Tails outcomes if you flip a coin 6 times: The roulette is a more complex appartus, but if you picture the head side of a coin being red and the tail side being black, you see that the possible outcomes are the same.
There are two possibilities for the first spin (or flip):
red or black
Again there are two possible results for the second spin,
red black / \ / \ red black red black
giving 2*2 = 4 possible outcomes for the first two spins.
For the third spin there are again two possible results
red black / \ / \ red black red black / \ / \ / \ / \ r bl r bl r bl r bl
giving 4*2 = 8 possible outcomes for the first three spins.
And so on: Each spin can yield two possible results, so the number of possible outcomes of 6 spins is 2*2*2*2*2*2 = 64.Claude