#### SOLUTION TO LAST MONTH'S QUIZ
1. 1/64
2. 7/256
3. 3/64
**Notes.**
Notation: H = Head, T = Tail, . = either
Total number of equi-probable permutations of H and T = 2^{10} = 1024
1. Number of perms. of form HHHHHH.... = 16
So probability = 16/1024 = 1/64
2. HHHHHHT... Number of perms. = 8
THHHHHHT.. Number of perms. = 4
.THHHHHHT. Number of perms. = 4
..THHHHHHT Number of perms. = 4
...THHHHHH Number of perms. = 8
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Total = 28
So probability = 28/1024 = 7/256
3. Using a similar method, find the number of permutations with exactly
six, seven, eight, nine and ten consecutive heads, and add. |