Perms/combination questions

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In summary, a permutation is an arrangement of objects in a specific order, while a combination is a grouping of objects without considering the order. Permutations are used when order matters, such as in a line-up or password combination, while combinations are used when order is not important, such as choosing a group of friends to go to a movie with. The formula for calculating permutations is nPr = n!/(n-r)!, where n is the total number of objects and r is the number of objects being selected. Most scientific or graphing calculators have a built-in function for calculating permutations and combinations. Permutations and combinations have real-life applications in many fields, including mathematics, statistics, computer science, and economics. Some examples include analyzing
  • #1
tofu
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here it is


Of the 21 young girls auditioning for the role of Annie, 9 were good dancers who couldnot sing well enough, but 5 could sing and dance well. Assuming that all girls possessed at least one of these skills, how many girls must have been good singers w/ out dancing skills
 
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  • #2
What have you tried to do to solve the problem?

(and should this be in homework help?)
 
  • #3
should be in homework or statistics section.

Are you saying out of 21 girls what is probability that when one is picked at random they are are good at singing but not dancing?
 

1. What is the difference between a permutation and a combination?

A permutation is an arrangement of a set of objects in a specific order, while a combination is a grouping of objects without considering the order. In a permutation, the order matters, while in a combination, it does not.

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

You should use a permutation when the order of the objects is important, such as in a line-up or a password combination. Use a combination when the order is not important, such as choosing a group of friends to go to a movie with.

3. What is the formula for calculating permutations?

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

4. Can I use a calculator to solve permutation and combination problems?

Yes, most scientific or graphing calculators have a built-in function to calculate permutations and combinations. Simply input the appropriate numbers and use the permutation or combination function.

5. Are there real-life applications for permutations and combinations?

Yes, permutations and combinations are used in many fields, including mathematics, statistics, computer science, and economics. Some examples include analyzing genetic codes, predicting outcomes in sports tournaments, and creating secure passwords.

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