Hello students, in this blog we are going to discuss the topic of permutations and combinations. These two topics are extensively used in mathematics.
Permutations: - The different arrangement of a given number of things by taking some or all at a time, are called the permutations. Let’s take a close look on the permutations.
All permutations made with the letter ‘a’, ‘b’, ‘c’ by taking two at a time are (ab, ba, ac, ca, bc, cb).
All permutations made with the letter ‘a’, ‘b’, ‘c’ by taking all at a time are (abc, acb, bac, bca, cab, cba).
Combinations: As name suggest of the combination that it is concept in which every number of separate groups are made by the when we include few or all number of an object, then it is known as the combination.
Suppose we want to select two out of three boys A, B, C. Then possible selections are AB, BC and CA.
Note that AB and BA represent the same selections.
Formula for permutation and combination are:
For permutation: “P r = n (n - 1) (n - 2)……(n –r + 1) = n! / (n - r) !,
Example for this: 1. 6 p2 =(6 * 5) = 30. 2. 7 P 3 = (7 * 6 * 5) = 210.
For combination: “C r = n ! / (r !) (n - r) ! = (n - 1) (n - 2)……to r factors / r !,
Example. 11 C 4 = (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1) = 330, (know more about icse board papers, here)
So applying both the formulas we can solve any permutation and combination problems.
In the next session we will discuss about Types of events.
Permutations: - The different arrangement of a given number of things by taking some or all at a time, are called the permutations. Let’s take a close look on the permutations.
All permutations made with the letter ‘a’, ‘b’, ‘c’ by taking two at a time are (ab, ba, ac, ca, bc, cb).
All permutations made with the letter ‘a’, ‘b’, ‘c’ by taking all at a time are (abc, acb, bac, bca, cab, cba).
Combinations: As name suggest of the combination that it is concept in which every number of separate groups are made by the when we include few or all number of an object, then it is known as the combination.
Suppose we want to select two out of three boys A, B, C. Then possible selections are AB, BC and CA.
Note that AB and BA represent the same selections.
Formula for permutation and combination are:
For permutation: “P r = n (n - 1) (n - 2)……(n –r + 1) = n! / (n - r) !,
Example for this: 1. 6 p2 =(6 * 5) = 30. 2. 7 P 3 = (7 * 6 * 5) = 210.
For combination: “C r = n ! / (r !) (n - r) ! = (n - 1) (n - 2)……to r factors / r !,
Example. 11 C 4 = (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1) = 330, (know more about icse board papers, here)
So applying both the formulas we can solve any permutation and combination problems.
In the next session we will discuss about Types of events.
The number of permutations of n distinct objects is n×(n − 1)×(n − 2)×...×2×1, which number is called "n factorial" and written "n!".permutation and combination
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