Arranging Letters of 'Daughter' with Specific Conditions

In summary, permutation and combination are different ways of arranging or selecting objects. Permutation considers the order of arrangement, while combination does not. To determine which to use, consider if order matters or not. The formula for calculating permutations is n!/(n-r)!, while the formula for calculating combinations is n!/(r!(n-r)!). Real-life examples of permutation and combination include lottery games and selecting sports teams.
  • #1
ritwik06
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Homework Statement



Arrange the letters of the word daughter such that
1. no two vowels are together.
2. the relative positions of the consonants and the vowels are not changed.





The Attempt at a Solution


1. Total arrangements =8!
Ways in which at least 2 vowels occur togther=7!*(3P2)
I subtract them, but my answer i different.
2. What does this statement mean?
 
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  • #2
Have I missed out something guys? Why isn't anybody paying any heed to ma question?
 
  • #3
ritwik06 said:
Have I missed out something guys? Why isn't anybody paying any heed to ma question?

Mods delete the thread...:cry:
 

What is the difference between permutation and combination?

The main difference between permutation and combination is the order of arrangement. Permutation is the arrangement of objects in a specific order, while combination is the selection of objects without considering the order.

How do I know when to use permutation or combination?

You should use permutation when the order of arrangement matters, such as finding the number of ways to arrange a set of letters or numbers. Combination should be used when the order does not matter, such as selecting a committee of people from a group.

What is the formula for calculating permutations?

The formula for calculating permutations is n!/(n-r)!, where n represents the total number of objects and r represents the number of objects being arranged.

What is the formula for calculating combinations?

The formula for calculating combinations is n!/(r!(n-r)!), where n represents the total number of objects and r represents the number of objects being selected.

Can you provide an example of when permutation or combination is used in real life?

Permutation is often used in lottery or gambling games, where the order of numbers matters. Combination is used in situations like selecting a team for a sports game, where the order of players does not affect the outcome.

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