Permutation and combination problem with coins

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SUMMARY

The discussion focuses on solving a permutation and combination problem involving coin flips. Specifically, it addresses finding the number of ways to obtain exactly two heads and at least two heads when a coin is flipped n times, where n is greater than or equal to 3. The key equations involve calculating arrangements of heads (H) and tails (T) using combinatorial principles. The user seeks clarity on applying these principles to derive the correct answers.

PREREQUISITES
  • Understanding of basic combinatorial principles
  • Familiarity with permutations and combinations
  • Knowledge of binomial coefficients
  • Basic probability concepts related to coin flips
NEXT STEPS
  • Study the concept of binomial coefficients in combinatorics
  • Learn how to calculate permutations and combinations using factorials
  • Explore the binomial theorem and its applications
  • Practice problems involving coin flip scenarios and their combinatorial solutions
USEFUL FOR

Students studying combinatorics, educators teaching probability concepts, and anyone looking to deepen their understanding of permutations and combinations in practical scenarios.

kenny1999
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Homework Statement



Hello, it is a permutation / combination approach question, however, having thought about an hour i can't get any idea how it should be solved.

Question is

A coin is flipped n times, where n>=3

Find the number of ways to obtain

(i) exactly two heads
(ii) at least 2 heads

I am not asking for answers. I have the answers but I don't understand... I don't know how to understand the problem from the definition of permutation and combination.

Homework Equations





The Attempt at a Solution

 
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To get exactly two heads, you must also get n- 2 tails. How many ways can you arrange HHTTTT...T?

"At least two heads" would mean "NOT 0 heads or 1 head". There are 2^n ways to arrange n letters that can be "H" or "T". How many ways are there to arrange HTTTT...T?
 

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