basic concepts of permutations and combinations
Question
basic concepts of permutations and combinations
Solution
Sure, here are the basic concepts of permutations and combinations:
- Permutations: Permutations refer to the arrangement of items in a specific order. The number of permutations of 'n' items taken 'r' at a time is given by the formula: nPr = n! / (n-r)!
For example, if you have three items A, B, and C, the permutations of these three items taken two at a time are AB, AC, BA, BC, CA, and CB. So, there are 6 permutations of 3 items taken 2 at a time.
- Combinations: Combinations refer to the selection of items without considering the order. The number of combinations of 'n' items taken 'r' at a time is given by the formula: nCr = n! / [(r!)(n-r)!]
For example, if you have three items A, B, and C, the combinations of these three items taken two at a time are AB, AC, and BC. So, there are 3 combinations of 3 items taken 2 at a time.
Note: 'n!' denotes the factorial of 'n', which is the product of all positive integers less than or equal to 'n'. For example, 5! = 54321 = 120.
Similar Questions
What is the main difference between a situation in which the use of the permutations rule is appropriate and one in which the use of the combinations rule is appropriate?Permutations count the number of different arrangements of r out of n items, while combinations count the number of groups of r out of n items.Both permutations and combinations count the number of groups of r out of n items. Combinations count the number of different arrangements of r out of n items, while permutations count the number of groups of r out of n items.Both permutations and combinations count the number of different arrangements of r out of n items.
For each of the following situations, explain why the combinations rule or the permutations rule should be used.(a) Determine the number of different groups of 5 items that can be selected from 12 distinct items.Use the combinations rule, since the number of arrangements within each group is of interest.Use the combinations rule, since only the items in the group is of concern. Use the permutations rule, since the number of arrangements within each group is of interest.Use the permutations rule, since only the items in the group is of concern.(b) Determine the number of different arrangements of 5 items that can be selected from 12 distinct items.Use the permutations rule, since the number of arrangements within each group is of interest.Use the combinations rule, since only the items in the group is of concern. Use the combinations rule, since the number of arrangements within each group is of interest.Use the permutations rule, since only the items in the group is of concern.
Which of the following types of permutation can be used when you want to know how many arrangements of letters can you make from the word MATHEMATICS?Group of answer choicesDistinct with RepetitionDistinct without RepetitionNondistinct PermutationCircular Permutation
There are 6 people in a raffle drawing. Two raffle winners each win gift cards. Each gift card is the same. How many ways are there to choose the winners?Decide if the situation involves a permutation or a combination, and then find the number of ways to choose the winners.A.Permutation; number of ways = 15B.Permutation; number of ways = 30C.Combination; number of ways = 15D.Combination; number of ways = 30SUBMITarrow_backPREVIOUS
There are 5 people in a raffle drawing. Two raffle winners each win gift cards. Each gift card is the same. How many ways are there to choose the winners?Decide if the situation involves a permutation or combination, and then find the number of ways to choose the winners.A.Permutation; number of ways = 20B.Combination; number of ways = 20C.Permutation; number of ways = 10D.Combination; number of ways = 10
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