Solving using permutation and combination

In summary: In this particular case, I think the combination of 5 consonants and 4 vowels gives the correct result.In summary, the book solves the problem using combination of 5 consonants and 4 vowels.
  • #1
rajeshmarndi
319
0

Homework Statement


From 5 consonants and 4 vowels, how many words can be formed consisting of 3 consonants and 2 vowels

The book solved it using combination
C(5,3) * C(4,2) * 5! = 7200

i.e I understand the 1st two term give the unique 5 words that can be formed with 5 consonants and 4 vowels and multiplying with 5! gives the permutation of all the 5 letters words

Homework Equations

The Attempt at a Solution


I tried on my own and used permutation
P(5,3) * P(4,2) = 720

I understand the book solution but then where am I wrong here?
 
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  • #2
rajeshmarndi said:

Homework Statement


From 5 consonants and 4 vowels, how many words can be formed consisting of 3 consonants and 2 vowels

The book solved it using combination
C(5,3) * C(4,2) * 5! = 7200

i.e I understand the 1st two term give the unique 5 words that can be formed with 5 consonants and 4 vowels and multiplying with 5! gives the permutation of all the 5 letters words

Homework Equations

The Attempt at a Solution


I tried on my own and used permutation
P(5,3) * P(4,2) = 720

I understand the book solution but then where am I wrong here?

Your method counts the vowels and consonants separately and doesn't take into account that they can then be mixed up. E.g. you could have:

##C_1C_5C_3## ##V_4V_2##

And there are then 10 ways to put these together into words with the vowels and consonants in that order.
 
  • #3
PeroK said:
Your method counts the vowels and consonants separately and doesn't take into account that they can then be mixed up. E.g. you could have:

##C_1C_5C_3## ##V_4V_2##

And there are then 10 ways to put these together into words with the vowels and consonants in that order.
Yes thanks, i.e C1C2C3 can be as such C1C2C3_ _ , C1 _ C2C3 _ , C1 _ _ C2C3 and so on.
 
  • #4
Just to add more, P(5,3) give C5C3C1 is counted once but it can be placed more than once in the 5 lettered words which I didn't counted as, C5_C3C1_ , C5_ _C3C1 and others similarly.
 
  • #5
Are these 5 distinct consonants and 4 distinct vowels? That's an important piece of information.
 
  • #6
HallsofIvy said:
Are these 5 distinct consonants and 4 distinct vowels? That's an important piece of information.
Yes I have been messing around, I had realized it lately.

The permutation of P(5,3) = 60 is at , say, 1st three position and along with it permutation of P(4,2) = 12 . This doesn't change location, say, of P(5,3) which can be placed in C(5,3) = 10 ways in the 5 lettered words, along with the permutation of P(4,2).

It then becomes P(5,3) * P(4,2) * C(5,3) = 60 * 12 * 10 = 7200.

Sometimes it becomes so hard to see how permutation/combination actually give the answer.
 

FAQ: Solving using permutation and combination

1. What is the difference between permutation and combination?

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

2. How do I know when to use permutation or combination?

Permutation is used when the order of the objects is important, such as in arranging letters in a word. Combination is used when the order is not important, such as in choosing a group of people for a team.

3. What is the formula for calculating permutations?

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

4. Can I use permutations and combinations in real life situations?

Yes, permutations and combinations are used in various fields such as mathematics, statistics, and computer science. They can also be applied in everyday situations, such as arranging seats at a dinner table or creating a password with a specific combination of characters.

5. Are there any restrictions when using permutations and combinations?

Yes, the objects being selected must be distinct and the total number of objects must be known. Additionally, repetition of objects is not allowed in permutations, but it is allowed in combinations.

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