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 April 9th, 2014, 07:00 PM #1 Senior Member   Joined: Jan 2009 Posts: 345 Thanks: 3 How many sequences contain 2 Tails and 3 Heads Confused about this one. I flip a coin 5 times. How many sequences have 2 tails and 3 heads? Is it Binomial[5,2]+Binomial[5,3] = 20? April 9th, 2014, 11:32 PM #2 Senior Member   Joined: Apr 2014 From: UK Posts: 965 Thanks: 342 I used finger-maths and added them up manually. these are the sequences with 2 tails 1,2 1,3 1,4 1,5 2,3 2,4 2,5 3,4 3,5 4,5 So the answer is 10 This is probably your Binomial[5,2]. The other half isn't required as it's implied, with 2 tails the other 3 must be heads anyway April 10th, 2014, 12:04 AM #3 Senior Member   Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra As there are only a handful of possibilities, we can list them all exhaustively: $\text{TTHHHH}$ $\text{THTHHH}$ $\text{HTTHHH}$ $\text{THHTHH}$ $\text{HTHTHH}$ $\text{HHTTHH}$ $\text{THHHTH}$ $\text{HTHHTH}$ $\text{HHTHTH}$ $\text{HHHTTH}$ $\text{THHHHT}$ $\text{HTHHHT}$ $\text{HHTHHT}$ $\text{HHHTHT}$ $\text{HHHHTT}$So there are $10$ possibilities. In general if a coin is thrown $n$ times, any sequence with exactly $r$ tails with have exactly $n-r$ heads and vice versa. So to find the number of sequences with exactly $r$ tails, compute EITHER $^n\mathrm C_r$ (tails) OR $^n\mathrm C_{n-r}$ (heads). Thanks from sivela Tags binomial, heads, sequences, tails Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Kuroniirp Probability and Statistics 6 October 6th, 2013 05:23 PM coolcat Advanced Statistics 1 November 27th, 2011 11:03 PM darandoma Algebra 3 September 22nd, 2011 10:35 PM slyone Algebra 2 September 5th, 2008 04:05 PM slyone Advanced Statistics 1 September 4th, 2008 06:13 AM

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