SOLUTION: Hi! This is part four of one of my homework problems and I only have one try left! I am so stumped. In an experiment, a fair coin is tossed 7 times and the face that appears (H for

Question 1123852: Hi! This is part four of one of my homework problems and I only have one try left! I am so stumped. In an experiment, a fair coin is tossed 7 times and the face that appears (H for head or T for tail) for each toss is recorded.
How many elements of the sample space will start or end with a head and have an adjacent pair or triple of heads and include a total of exactly three heads?
I had the idea that there are only a few cases this can true, when H is first, last, or both first and last.
HH is first: 5
HH(any combination of TTTTH, so 5 possibilities)
HH is last: 5
(any combination of TTTTH, so 5 possibilities)HH
H is first and last: 2
H(TTTTT)HH or HH(TTTTT)H
HHH is first: 1
(HHH)(TTTT)
HHH is last: 1
(TTTT)(HHH)
I think the answer is 14, I haven't tried that answer yet because I miscounted the last try and said 12. If someone could confirm this answer/logic or explain a different answer that would be amazing!!!

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i count 16

actually 18, but 2 of them are duplicates, so 16 unique.

i checked 3000 times so i'm pretty sure the count is accurate.

here's my worksheet.

$$$

first i looked at the ones that started with 3 heads.
then i looked at the ones that ended with 3 heads.
then i looked at the ones that started with 2 heads.
then i looked at the ones that ended with 2 heads.
then i looked at the ones that started with 1 head.
then i looked at the ones that ended with 1 head.

the spreadsheet is organized in that manner.
the ones in red were the duplicates.
i did an eyeball scan and i also gave each set a numeric code.
if the codes was the same, those were duplicates, as confirmed by an eyeball check.

if i were you, i would go with 16.
hopefully that will do the trick.

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