Permutation and combination problem with coins

In summary, the question is asking for the number of ways to obtain exactly two heads and at least two heads when a coin is flipped n times, using a permutation/combination approach. To obtain exactly two heads, there are n-2 tails in the arrangement. For at least two heads, the number of possible arrangements is found by subtracting the number of arrangements with 0 or 1 head from the total number of possible arrangements.
  • #1
kenny1999
235
4

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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  • #2
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 [itex]2^n[/itex] ways to arrange n letters that can be "H" or "T". How many ways are there to arrange HTTTT...T?
 

FAQ: Permutation and combination problem with coins

What is the difference between permutation and combination?

Permutation refers to the arrangement of objects in a specific order, while combination refers to the selection of objects without considering the order in which they are chosen.

How many ways can you arrange a set of coins?

The number of ways to arrange a set of coins can be calculated using the formula n!, where n is the number of coins. For example, if you have 4 coins, there are 4! or 24 ways to arrange them.

What is the formula for calculating permutations?

The formula for calculating permutations is n! / (n - r)!, where n is the total number of objects and r is the number of objects being selected. This is also known as the "n choose r" formula.

How do I know whether to use permutation or combination in a problem?

You should use permutation when the order of the objects matters, and combination when the order does not matter. For example, if you are arranging coins in a specific order, you would use permutation. If you are selecting coins without considering the order, you would use combination.

Can permutation and combination be applied to real-world problems?

Yes, permutation and combination can be applied to real-world problems such as arranging seats at a dinner party or selecting a team for a sports tournament. These concepts are also used in fields such as statistics, probability, and genetics.

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