Permutations and Combinations - Some useful Formulae

·  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.

Examples:

       i.            We define 0! = 1.

     ii.            4! = (4 x 3 x 2 x 1) = 24.

  iii.            5! = (5 x 4 x 3 x 2 x 1) = 120.

·  Permutations:

The different arrangements of a given number of things by taking some or all at a time, are called permutations.

Examples:

       i.            All permutations (or arrangements) made with the letters a, b, c by taking two at a time are (ab, ba, ac, ca, bc, cb).

     ii.            All permutations made with the letters a, b, c taking all at a time are:
( abc, acb, bac, bca, cab, cba)

·  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)!

Examples:

       i.            ⁶P₂ = (6 x 5) = 30.

     ii.            ⁷P₃ = (7 x 6 x 5) = 210.

  iii.            Cor. number of all permutations of n things, taken all at a time = n!.

·  An 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 p_r are alike of r^th kind,
such that (p₁ + p₂ + ... p_r) = n.

Then, number of permutations of these n objects is =	n!
	(p1!).(p2)!.....(pr!)

·  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.

Examples:

1.     Suppose 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.

2.     All the combinations formed by a, b, c taking ab, bc, ca.

3.     The only combination that can be formed of three letters a, b, c taken all at a time is abc.

4.     Various groups of 2 out of four persons A, B, C, D are:

AB, AC, AD, BC, BD, CD.

5.     Note that ab ba are two different permutations but they represent the same combination.

·  Number of Combinations:

The number of all combinations of n things, taken r at a time is:

nCr =	n!	=	n(n - 1)(n - 2) ... to r factors	.
	(r!)(n - r!)		r!

Note:

       i.            ⁿC_n = 1 and ⁿC₀ = 1.

     ii.            ⁿC_r = ⁿC_{(n - r)}

Examples:

i.   11C4 =	(11 x 10 x 9 x 8)	= 330.
	(4 x 3 x 2 x 1)

ii.   16C13 = 16C(16 - 13) = 16C3 =	16 x 15 x 14	=	16 x 15 x 14	= 560.
	3!		3 x 2 x 1

SSC CGL 2013 - General Intelligence - Answer Key

1)      X goes 15 metres North, then turns right and walks 20 metres, then again turns right and walks 10 metres then again turns right and walks 20 metres. How many metres is he from his original position?

a)      5 metres

b)      10 metres

c)      15 metres

d)     20 metres

2)      A watch reads 7:30. If the minute hand points West, which direction will the hour hand point?

a)      North

b)      North East

c)      North West

d)     South East

In Questions 3 to 5, from the given alternative words select the which cannot be formed using the letters of the given word.

3)      PENULTIMATE

a)      PEANUT

b)      MINUTE

c)      ELIMINATE

d)     LIME-TEA

4)      PROCRASTINATE

a)      PATTERN

b)      TRACTOR

c)      PRINTED

d)     PAINTER

5)      ADOLESCENT

a)      ENCLOSE

b)      DONATE

c)      SECRET

d)     LEAST

6)      IF SPANK is coded as PSNAK, then THROW is coded as

a)      HTWOR

b)      HTWRO

c)      HTROW

d)     HTORW

7)      If ANCIENT is coded as 2516859 and NATURE is coded as 529048, then TRAIN will be coded as:

a)      94285

b)      92456

c)      94265

d)     94168

8)      If BLUE is written as EUBL, then BULB is written as:

a)      BLUB

b)      BBUL

c)      BBLU

d)     BLBU

9)      40% of 1620 + 30% of 960 = ? % of 5200

a)      12

b)      24

c)      16

d)     18

10)  Which of the following interchange of signs would make the given equations correct?

2 x 3 + 6 – 12 /4 = 17

a)      x and +

b)      + and –

c)      + and /

d)     – and /

11)  ‘B’ stands for addition, ‘G’ stands for subtraction, ‘E’ stands for multiplication, ‘C’ stands for division, ‘D’ stands for equal to, ‘A’ stands for greater than, ‘F’ stands for less than. In each of the following alternatives, only one expression is correct according to the letter symbol. Identify that expression

a)      15 C 3 B 2 A 6 E 2

b)      15 B 2 G 5 A 4 G 4

c)      15 C 3 B 2 D 6 B 1

d)     15 B 3 D 4 E 6

12)  Identify the symbols that are to inserted to make the expression correct

24 @ 4 @ 5 @ 4

a)      x + x

b)     = x +

c)      x + =

d)     + = x

In questions 13 to 18, find the related word/number from the given alternatives:

13)  Video: Cassette :: Computer : ?

a)      Files

b)      Floppy

c)      Bits

d)     Adit

14)  Glucometer: Blood Sugar :: Sphygmomanometer : ?

a)      Earthquake

b)     Blood Pressure

c)      Atmospheric Pressure

d)     Specific Gravity

15)  Behaviour : Psychology :: Plant : ?

a)      Plant

b)     Botany

c)      Zoology

d)     Physiology

16)  Mitochondria : Energy :: DNA : ?

a)      Inheritance

b)      Reproduction

c)      Locomotion

d)     Immunity

17)  Desert : Mirage :: Ocean : ?

a)      El-Nino

b)      Whale

c)      Blizzard

d)     Hail

18)  525 : 25 :: 315 : ?

a)      10

b)     15

c)      5

d)     25

Directions: In questions 19 to 24, find the odd word/number/letters/ number pair from the given alternatives.

19)  a) 3/7   b) 7/2   c) 4/13 d) 13/16

20)  a) Marine         b) Ocean          c) Navigation  d) Sea

21)  a) ZYX            b) FED                        c) NML           d) GHI

22)  a) XZY            b) MON          c) PRQ                        d) EAC

23)  a) 1-5               b) 4-20             c) 5-65             d) 7-35

24)  a) 46-10           b) 42-33           c) 20-38           d) 91-12

Directions: In question nos. 25 and 26, arrange the given words a meaningful and ascending order and select the option indicating the correct order:

25)  1. Venus          2. Earth           3. Mars            4. Mercury       5. Jupiter

a)      4,2,1,3,5    b) 4,2,1,5,3      c) 4,1,2,3,5      d) 4,1,2,5,3

26)  1. Pages           2. Book Rack  3. Library        4. Books          5. Catalogue

a)      2,5,4,3,1    b) 1,5,4,3,2      c) 1,4,2,5,3      d) 1,2,4,5,3

27)  Which one set of letters when sequentially placed at the gaps in the given letter series shall complete it?

ab_babc_ab_b_bcb_b

a)      cbcaa        b) cabac           c) abcba           d) acaca

28)  A series is given, with on eterm missing. Choose the correct alternative from the given ones.

ABEF, IJMN, ?

a)      QRVU      b) QRUV        c) QRVW        d) QSVU

Directions. In questions 29 to 3, find the missing number from the given responses.

29)  0,6,24,60,?,210

a)      117

b)      119

c)      120

d)     153

30)  49        81        64

4          49        9

25        16        36

10        ?          11

a) 6      b) 4      c) 9      d) 16