Permutations/combinations help

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In summary, the conversation is about a problem involving permutations and combinations in braille code. The question asks how many symbols can be represented in braille with at least one raised dot, and the answer is 63. Two different methods are provided to arrive at this answer, using either 2^6-1 or 6 choose 1, 2, 3, 4, 5, and 6. The conversation then moves on to discussing how many combinations have exactly 3 raised dots and an even number of raised dots, with the answers being 20 and 28 respectively.
  • #1
roadrunner
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permutations/combinations help please

Hello everyone im' stuck on this problem.

It says:
Each symbol in braille code is represened by a rectangular arrangement of six dots. Given that a least 1 dot of the 6 must be raised, how many symbols can be represented in brail?

now i saw this posted somewhere else, they got 63. don't know how.

i got 63 two ways...

2^6-1 (case where all down)=63

6c1+6c2+6c3+6c4+6c5+6c6 -1 also =63 (where 6c3 etc is combinations...6 options choose 3)

can sumone explain how/why that works please.

also part b...how many combinations have EXACTLY 3 raised

and how many have an even number of raised dots
 
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  • #2
roadrunner said:
Hello everyone im' stuck on this problem.

How are you stuck? You gave two good answers to the question, both of which are correct and correctly explained. The second approach gives a direct answer to your other questions -- 6 choose 3 ways to have three raised, and the appropriate combinations for only even ones raised.
 
  • #3
im stuck on part b lol exactly 3 rasied
is is 6c3=20?
and part c...how many symbols have an even number of raised dots...
so 6c2+6c4+6c6?
 

1. What is the difference between permutations and combinations?

Permutations and combinations both involve arranging or selecting elements from a set, but the key difference is that permutations take into account the order of the elements, while combinations do not. In other words, permutations are ordered arrangements, while combinations are unordered selections.

2. How do I calculate the number of permutations or combinations?

The number of permutations of n objects taken r at a time can be calculated using the formula n!/(n-r)!, while the number of combinations of n objects taken r at a time can be calculated using the formula n!/r!(n-r)!. In both cases, n represents the total number of objects and r represents the number of objects being selected.

3. What is the significance of permutations and combinations in probability and statistics?

Permutations and combinations are fundamental concepts in probability and statistics. They are often used to calculate the probability of certain outcomes or events, as well as to analyze data and make statistical inferences. For example, in a lottery, the number of possible combinations can be calculated to determine the odds of winning.

4. How can I apply permutations and combinations in real life situations?

Permutations and combinations can be used in various real-life situations, such as in sports tournaments, seating arrangements, and password combinations. They are also useful in solving problems related to combinations of colors, shapes and sizes, and in determining the number of possible outcomes in a game or experiment.

5. Are there any common mistakes to avoid when working with permutations and combinations?

One common mistake is confusing permutations with combinations, as they have different formulas and results. Another mistake is forgetting to consider whether repetition is allowed in the arrangement or selection. It is also important to carefully read the problem and identify whether it is a permutation or combination problem, as the approach to solving them may differ.

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