DEPARTMENT OF TRAINING & PLACEME
“FACTORIAL”
A factorial is a mathematical function that multiplies a number by
every number that comes before it, down to 1:
Symbol: Factorials are represented by an exclamation mark, for
example, 4!.
Formula: The formula for a factorial is n!=n(n-1).
Examples: 4! = 4 x 3 x 2 x 1 = 24, and 5! = 5 x 4 x 3 x 2 x 1 = 120.
Factorial of zero: 0! Is defined as 1
N!= n * (n-1) * (n-2) * (n-3) **3*2*1
0! = 1
1! = 1
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6
4! = 4 x 3 x 2 x 1 =24
“ PERMUTATIONS ”
A permutation is a mathematical concept that describes the number
of ways to arrange a set of data in a specific order. The order of the
data is important in a permutation, as is the case with a safe or
locker combination.
Formula
nPr = n !/(n-r) !
n Pr = permutation
N = total number of objects
R = number of objects selected
The possible permutations of 1, 2 and 3 are 123,132, 213, 231, 312
and 321.
Total 6 ways are possible
The Permutation of n objects taken n at a time is: nPr = n! (n-r)!
Example 1.
Evaluate: 5P3
Solution.
N = 5, r = 3
nPr = n!/(n-r)!
5P3 = 5!/(5-3)!
5! /2! =5×4×3×2×1/2×1
=60
TYPE-1 ( WORD FORMATION)
1- In how many different ways can the letters of the word HOME
be arranged?
2- In how many different ways can the letters of the word APPLE
be arranged?
3- In how many different ways can the letters of the word
TAMANNA be arranged?
4- In how many different ways can the letters of the word
‘NATIONAL’ be arranged?
5- How many words can be formed using all the letters of the
word “ABHISHEK’ so that all the three vowels should come
together?
6- How many words can be formed using all the letters of the
word “SUCCESS’ so that all vowels should come together?
7- How many words can be formed using all the letters of the
word ‘NATION’ so that all the three vowels should never come
together?
8- How many words can be formed from the letters of the word
9-How many words beginning with vowels can be formed using
letters of the word DAUGHTER?
10-In how many different ways can the letters of the word SUBJECT
be arranged so that the vowels are at the two ends?
11-In how many different ways can the letters of the word NATION
be arranged so that the vowels occupy at the even places?
12-How many words (with or without meaning) can be formed from
the letters of the word, ‘DAUGHTER’, so that
(i) All vowels occur together?
(ii) All vowels do not occur together?
13-How many words can be made from the word IMPORTANT in
which both T do not come together?
14-How many different words can be formed with the letters of the
word NAINITAL such that each of the word begin with L and end with
T?
15-In how many ways can the word CHRISTMAS be arranged so that
the letters C and M are never adjacent?
16-In how many ways can we sort the letters of the word
MANAGEMENT so that the comparative position of vowels and
consonants remains the same as in MANAGEMENT.
TYPE-2 NUMBER ARRANGEMENT
17- By using the digits (1, 3, 4, 5, 6, 7, 8) how many five digit numbers
can be made? Rule* (Recurrence of numbers is not allowed)?
18-How many possible two-digit numbers can be formed by using
the digits 3, 5 and 7 (repetition of digits is allowed)?
19-How many 3 digit odd numbers can be formed from the digits 5, 6,
7, 8, 9, if the digits can be repeated?
20-How many four-digit numbers can be formed with digits 2, 5, 6, 7
and 8? (Repeating digits are not allowed)
21-The number of ways of arrangements of 10 persons in four chairs
is –
22-. Out of numbers (1, 2,3,5,7 & 9) how many four digit even
numbers can be formed?
23-How many numbers are there between 99 and 1000, having at
least one of their digits 7?
24-How many 5-digit telephone numbers can be constructed using
the digits 0 to 9, if each number starts with 67 and no digit appears
more than once?
25-How many numbers between 999 and 4000 can be formed with
the digits 0, 1, 2, 3 and 4 if repetitions of digits is allowed?
TYPE-3 GROUP ARRANGMENT
26- In how many ways 5 boys and 4 girls can be seated in a row?
27-In how many ways 5 boys and 4 girls can be seated in a row so
that no two girls are together?
28-5 men and 4 women are to be seated in a row so that the women
occupy the even places. How many such arrangements are possible?
29-Find out the number of ways in which 6 male teachers and 6
female teachers can be settled on seat for a shoot so that no two
female teachers sit together?
30-In how many ways 4 boys and 4 girls can be seated in a line boys
and girls sit one after the other.
TYPE-4 ( LOCK PATTERN)
Total code -10^n
Total wrong code =10^n-1
31-How can the four digits code be made inside the box?
32-How many ATM password are possible ?
33-A boy forgot last 4 digit of any mobile numbers. How many wrong
number can he dial?
34-device password comprises 5 rings each having 7 different
messages. Find out the maximum number of different unsuccessful
efforts to open the lock?
35-A boy forgot last 4 digit of any mobile numbers. How many wrong
number can he dial?
TYPE-5. CIRCULAR ARRANGEMENT
Total no of value =N!
So Arrangment=(N-1)!
If you create neckless =(n-1)!/2
31 -How many ways to arrange 9.C.M. around a circular table, if the
C.M. of Punjab and Haryana always sit together?
32-How many necklace can be form with 6 red and 5 blue Flower?
33-6 Friends how many ways can you sit around a circular in the
circle?
34-In how many ways five people A,B,C,D and E
Be seated around a circular table if A And B
Must not sit next to each other?
35-In how many ways can 8 people be seated at a round table?
TYPE-5 GIFT DISTRIBUTION
36-How many ways to distribute 3 different awards among 10
students?
37-Ten students are participating a race. In how many ways can the
first 3 prizes be won?
38-8 students are participating in a competition. In how many ways
can the first three prizes be won?
39-Twelve students compete in a race. In how many ways first three
prizes be given?
40-In how many ways can 3 letters be put in a 5 letter box.
