Permutation and combination problem with coins

AI Thread Summary
The discussion revolves around a permutation and combination problem involving coin flips. The main question is how to calculate the number of ways to achieve exactly two heads and at least two heads when a coin is flipped n times, with n being greater than or equal to three. To find exactly two heads, one must consider the arrangement of two heads and n-2 tails. For at least two heads, the calculation involves subtracting the scenarios of zero and one head from the total arrangements of n flips, which is 2^n. Understanding these concepts is crucial for solving the problem effectively.
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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