Aptitude Quiz - Important Formulas

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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.


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.


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)!


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!


i.  nCn = 1 and nC0 = 1.

ii. nCr = nC(n - r)


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.


We define 0! = 1.

3! = (3 x 2 x 1) = 6.

Go through Our Important Topics:

Interview Tips           Abbreviations            Dates To Remember

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