PPT - Permutations & Combinations

# PPT - Permutations & Combinations - Business Mathematics and Statistics - B Com

``` Page 1

1)  Permutation
2)  Combination
Permutations and Combinations
Permutations and Combinations
?
Determine probabilities using permutations.
?
Determine probabilities using combinations.
Page 2

1)  Permutation
2)  Combination
Permutations and Combinations
Permutations and Combinations
?
Determine probabilities using permutations.
?
Determine probabilities using combinations.
Permutations and Combinations
Permutations and Combinations
An arrangement or listing in which order or placement is important is called a
permutation.
Simple example:    “combination lock”
31 – 5 – 17         is NOT  the same as           17 – 31 – 5
Page 3

1)  Permutation
2)  Combination
Permutations and Combinations
Permutations and Combinations
?
Determine probabilities using permutations.
?
Determine probabilities using combinations.
Permutations and Combinations
Permutations and Combinations
An arrangement or listing in which order or placement is important is called a
permutation.
Simple example:    “combination lock”
31 – 5 – 17         is NOT  the same as           17 – 31 – 5
Permutations and Combinations
Permutations and Combinations
An arrangement or listing in which order or placement is important is called a
permutation.
Simple example:    “combination lock”
31 – 5 – 17         is NOT  the same as           17 – 31 – 5
Though the same numbers are used, the order in which
they are turned to, would mean the difference in the lock
opening or not.
Thus, the order is very important.
Page 4

1)  Permutation
2)  Combination
Permutations and Combinations
Permutations and Combinations
?
Determine probabilities using permutations.
?
Determine probabilities using combinations.
Permutations and Combinations
Permutations and Combinations
An arrangement or listing in which order or placement is important is called a
permutation.
Simple example:    “combination lock”
31 – 5 – 17         is NOT  the same as           17 – 31 – 5
Permutations and Combinations
Permutations and Combinations
An arrangement or listing in which order or placement is important is called a
permutation.
Simple example:    “combination lock”
31 – 5 – 17         is NOT  the same as           17 – 31 – 5
Though the same numbers are used, the order in which
they are turned to, would mean the difference in the lock
opening or not.
Thus, the order is very important.
Permutations and Combinations
Permutations and Combinations
The manager of a coffee shop needs to hire two employees, one to work at the
counter and one to work at the drive-through window.  Sara, Megen, Tricia and Jeff
all applied for a job.  How many possible ways are there for the manager to place
the applicants?
Page 5

1)  Permutation
2)  Combination
Permutations and Combinations
Permutations and Combinations
?
Determine probabilities using permutations.
?
Determine probabilities using combinations.
Permutations and Combinations
Permutations and Combinations
An arrangement or listing in which order or placement is important is called a
permutation.
Simple example:    “combination lock”
31 – 5 – 17         is NOT  the same as           17 – 31 – 5
Permutations and Combinations
Permutations and Combinations
An arrangement or listing in which order or placement is important is called a
permutation.
Simple example:    “combination lock”
31 – 5 – 17         is NOT  the same as           17 – 31 – 5
Though the same numbers are used, the order in which
they are turned to, would mean the difference in the lock
opening or not.
Thus, the order is very important.
Permutations and Combinations
Permutations and Combinations
The manager of a coffee shop needs to hire two employees, one to work at the
counter and one to work at the drive-through window.  Sara, Megen, Tricia and Jeff
all applied for a job.  How many possible ways are there for the manager to place
the applicants?
Permutations and Combinations
Permutations and Combinations
The manager of a coffee shop needs to hire two employees, one to work at the
counter and one to work at the drive-through window.  Sara, Megen, Tricia and Jeff
all applied for a job.  How many possible ways are there for the manager to place
the applicants?
Counter              Drive-Through                 Outcomes
Sara
Megen
Tricia
Jeff
```

115 videos|142 docs

## FAQs on PPT - Permutations & Combinations - Business Mathematics and Statistics - B Com

 1. What is the difference between permutations and combinations?
Ans. Permutations and combinations are both methods used to calculate the number of possible outcomes in a given situation. The main difference between them lies in the order in which the items are arranged. Permutations consider the order of arrangement, while combinations do not.
 2. How do permutations and combinations relate to probability?
Ans. Permutations and combinations are closely related to probability as they help in calculating the number of favorable outcomes in a sample space. By using these concepts, we can determine the probability of an event occurring by dividing the number of favorable outcomes by the total number of possible outcomes.
 3. Can you provide an example of a permutation problem?
Ans. Sure! Let's say we have 5 people (A, B, C, D, and E) and we want to arrange them in a line. The number of permutations can be calculated using the formula nPr = n! / (n - r)!, where n is the total number of items and r is the number of items to be arranged. In this case, the number of permutations would be 5P5 = 5! / (5 - 5)! = 5!.
 4. How do combinations work when dealing with a group of items?
Ans. Combinations are used when we want to select a group of items without considering the order. For example, if we have 5 fruits (apple, banana, cherry, durian, and elderberry) and we want to choose 3 fruits, we can calculate the number of combinations using the formula nCr = n! / (r! * (n - r)!), where n is the total number of items and r is the number of items to be chosen. In this case, the number of combinations would be 5C3 = 5! / (3! * (5 - 3)!).
 5. How are permutations and combinations used in real-life scenarios?
Ans. Permutations and combinations have various applications in real-life scenarios. They are used in fields such as statistics, probability, genetics, computer science, and cryptography. For example, in genetics, permutations are used to calculate the possible genetic outcomes of offspring. In computer science, combinations are used in algorithms to generate all possible combinations of a set of elements.

115 videos|142 docs

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