2010-08-12, 06:06 PM
^ in fact you can envision it as Pascal's triangle.
Every row represents a coin flip. For each heads you go down and to the left, for each tails you go down and to the right. Reading across the rows tells you the number of permutations possible for each split of heads and tails.
In particular, there are 252 permutations of 5 heads and 5 tails, so it has a 252/1024 chance (just under 1/4) of occurring.
Every row represents a coin flip. For each heads you go down and to the left, for each tails you go down and to the right. Reading across the rows tells you the number of permutations possible for each split of heads and tails.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1
In particular, there are 252 permutations of 5 heads and 5 tails, so it has a 252/1024 chance (just under 1/4) of occurring.