Bob
grade 12

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.....

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.