Bankers Adda is also known to be called as Aptitude Quiz adda.
Today Bankers Adda came back with a New Quiz on Aptitude
Go through the quiz and if you have any doubts please contact bankers adda in the comment section.
Important Formulas - Permutations and Combinations:
1. Important Result:
If there are n subjects of which p1 are alike of one kind; p2 are alike of another kind; p3 are alike of third kind and so on and pr are alike of rth kind,
such that (p1 + p2 + ... pr) = n.
Then, number of permutations of these n objects is = n!/(p1!).(p2)!.....(pr!)
2. Permutations:
The different arrangements of a given number of things by taking some or all at a time, are called permutations.
Ex:
i. All permutations made with the letters a, b, c taking all at a time are: ( abc, acb, bac, bca, cab, cba)
ii.All permutations (or arrangements) made with the letters a, b, c by taking two at a time are :(ab, ba, ac, ca, bc, cb).
3. Combinations:
Each of the different groups or selections which can be formed by taking some or all of a number of objects is called a combination.
Ex:
i. If we want to select two out of three boys A, B, C. Then, possible selections are AB, BC and CA.
Note: AB and BA represent the same selection.
ii. All the combinations formed by a, b, c taking ab, bc, ca.
iii.The only combination that can be formed of three letters a, b, c taken all at a time is abc.
iv. Various groups of 2 out of four persons A, B, C, D are:
AB, AC, AD, BC, BD, CD.
v. Note that ab ba are two different permutations but they represent the same combination.
4. Number of Permutations:
Number of all permutations of n things, taken r at a time, is given by:
nPr = n(n - 1)(n - 2) ... (n - r + 1) = n!/(n - r)!
Ex:
i. 4P2 = (4 x 3) = 12.
ii.5P3 = (5 x 4 x 3) = 60.
5. Number of Combinations:
The number of all combinations of n things, taken r at a time is:
nCr = n!/(r!)(n - r)! = n(n - 1)(n - 2) ... to r factors/r!
Note:
i. nCn = 1 and nC0 = 1.
ii. nCr = nC(n - r)
Ex:
i. 11C4 = (11 x 10 x 9 x 8)/(4 x 3 x 2 x 1) = 330.
ii. 16C13 = 16C(16 - 13) = 16C3 = 16 x 15 x 14/3! = 16 x 15 x 14/3 x 2 x 1 = 560.
6. Factorial Notation:
Let n be a positive integer. Then, factorial n, denoted n! is defined as:
n! = n(n - 1)(n - 2) ... 3.2.1.
Ex:
We define 0! = 1.
3! = (3 x 2 x 1) = 6.
Go through Our Important Topics:
Today Bankers Adda came back with a New Quiz on Aptitude
Go through the quiz and if you have any doubts please contact bankers adda in the comment section.
Important Formulas - Permutations and Combinations:
1. Important Result:
If there are n subjects of which p1 are alike of one kind; p2 are alike of another kind; p3 are alike of third kind and so on and pr are alike of rth kind,
such that (p1 + p2 + ... pr) = n.
Then, number of permutations of these n objects is = n!/(p1!).(p2)!.....(pr!)
2. Permutations:
The different arrangements of a given number of things by taking some or all at a time, are called permutations.
Ex:
i. All permutations made with the letters a, b, c taking all at a time are: ( abc, acb, bac, bca, cab, cba)
ii.All permutations (or arrangements) made with the letters a, b, c by taking two at a time are :(ab, ba, ac, ca, bc, cb).
3. Combinations:
Each of the different groups or selections which can be formed by taking some or all of a number of objects is called a combination.
Ex:
i. If we want to select two out of three boys A, B, C. Then, possible selections are AB, BC and CA.
Note: AB and BA represent the same selection.
ii. All the combinations formed by a, b, c taking ab, bc, ca.
iii.The only combination that can be formed of three letters a, b, c taken all at a time is abc.
iv. Various groups of 2 out of four persons A, B, C, D are:
AB, AC, AD, BC, BD, CD.
v. Note that ab ba are two different permutations but they represent the same combination.
4. Number of Permutations:
Number of all permutations of n things, taken r at a time, is given by:
nPr = n(n - 1)(n - 2) ... (n - r + 1) = n!/(n - r)!
Ex:
i. 4P2 = (4 x 3) = 12.
ii.5P3 = (5 x 4 x 3) = 60.
5. Number of Combinations:
The number of all combinations of n things, taken r at a time is:
nCr = n!/(r!)(n - r)! = n(n - 1)(n - 2) ... to r factors/r!
Note:
i. nCn = 1 and nC0 = 1.
ii. nCr = nC(n - r)
Ex:
i. 11C4 = (11 x 10 x 9 x 8)/(4 x 3 x 2 x 1) = 330.
ii. 16C13 = 16C(16 - 13) = 16C3 = 16 x 15 x 14/3! = 16 x 15 x 14/3 x 2 x 1 = 560.
6. Factorial Notation:
Let n be a positive integer. Then, factorial n, denoted n! is defined as:
n! = n(n - 1)(n - 2) ... 3.2.1.
Ex:
We define 0! = 1.
3! = (3 x 2 x 1) = 6.
Go through Our Important Topics:
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