Permutations and combinations are two important methods of arranging and grouping items. A permutation is an arrangement of items in a specific order, while a combination is a grouping of items without regard to order.
This means that the order in which the items are placed in a permutation is important, as the same items placed in a different order would result in a different permutation, while in a combination the order is not important and the same items placed in a different order would still result in the same combination.
Permutations and combinations can be used to solve a variety of problems, from counting the number of possible outcomes in a given situation to determining the probability of certain events occurring.
A permutation in Maths is when you take a given set of numbers or objects and rearrange them in a different order. This could be done in any number of ways, depending on the number of items in the set.
For example, if you had three items in a set, you could rearrange them in six different ways. By using permutations, you can determine the number of possible outcomes in a given situation and calculate the probability of certain events occurring.
Permutation Formula:
nPr = permutation
n = total number of objects
r = number of objects selected
Let's say you have three fruits - an apple, a banana, and a cherry. You can arrange them in different orders, just like how you can arrange letters in the alphabet. For example, you can arrange them as ABC (apple, banana, cherry), or you can arrange them as ACB (apple, cherry, banana). There are six different arrangements you can make in total: ABC, ACB, BAC, BCA, CAB, and CBA.
Combination in Maths is when you combine two or more numbers or objects to create a different result than what you would get if you used the same items separately.
Combinations allow you to explore possible outcomes in a given situation and can be used to calculate the probability of certain events occurring.
Combination Formula:
nCr = number of combinations
n = total number of objects in the set
r = number of choosing objects from the set
Suppose you have four different books, A, B, C, and D. You want to choose two books to read. The possible combinations are AB, AC, AD, BC, BD, and CD.
Permutation | Combination |
Order matters | Order does not matter |
The arrangement is different | The arrangement is the same |
Example: Picking a president, vice-president, and secretary of a club | Example: Choosing 3 friends to play with |
The number of arrangements is greater | The number of arrangements is smaller |
Permutation formula: n!/(n-r)! | Combination formula: n!/r!(n-r)! |
Repetition is not allowed | Repetition is allowed |
Example: The order in which colors are chosen | Example: The colors chosen |
nPr is always greater than or equal to nCr | nCr is always less than or equal to nPr |
Permutations and combinations can be applied to a variety of real-world scenarios like,
In conclusion, permutations and combinations are powerful methods of arranging and grouping items that can be used to solve a variety of problems. Whether it's counting the number of possible outcomes in a given situation, determining the probability of certain events occurring, or even making decisions like what to wear or what movie to watch, understanding permutations and combinations can be a valuable tool.
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
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