Permutation-:Permutation is the arrangement of
Items in which Ordered is matter.
Numbers 0f ways selection and arrangement of items in
which ordered matter.
N rP= n!
(n-r)!
1.How many ways 10 people line up at a ticket window of a cinema
hall?
2.How many word ,with or without meanings can
be formed using all letters of words EQUATION.
Using each letter exactly once.
3.How many different signals can be using any
number of flags from 5 flags of different color.
5!/4!+5!/3!+5!/2!+5!/1!+5!=Ans.
4.In How many ways can 5 men and 4 women be
seated in a rows .so women occupy the even
places .
4! 5!=Ans.
5.How many Four digits Number can be formed by
using the digits 1 to 9 if repetition of digits is not
allowed.
6.i=>How many different number of six digit can
be formed with the number 3,1,7,0,9,5.->>6!-5!
ii. How many them of are divisible by 10.->>5!
7. i. >In how many ways letter of UNIVERSAL can
be Arrange .
ii. In how Many ways these will ERS always occur
together?==>U N I V A L ERS 7!*3!
8.How many ways word can be formed from the
letter of the word DAUGHTER .
i. Taking the All letter together.=>8!
ii. Beginning With D.=>7!
iii. Beginning With D and Ending with R.=>6!
iv. Vowel is being always together.=D G H T R AUE
6!*3!.
9.How Many different words can be formed out of
the letter of word MALENKOV .so that
i. First letter is vowel. =>3p1 * 7!
ii. No two Vowels are together =>5!*6p3.
iii. relative position of vowel and constant remains
unchanged.3!*5!
Repetition problems
10.In how many ways can different six rings can
worn on four fingers of a hand.=>46 ways .
11.In how many ways can 6 apples be distributed
among 3 boys .there being no restriction to the
number of apples each boys may get.
36 ways
12.In how many ways 3 prizes distributed among
four boys when
I .a boys may get any number of prizes .
ii. No boys ger all the prizes. -> 43-4ways
13.How many 3 digits Number can form using
digits
a.1,2,6,8 =>43 b. 0,2,3,6,8=>4*5*5
14.How many arrangements can be made of the
letter of the ‘ARRANGEMENT’ .in how many of
these vowels occur together.
=>10! ,,,,,,=>R R N G M N T A A E E =>8!*4!
Circular pemutations
15.In how many ways 6 persons can be seated .
I. In a line=>6! ii. In a round tables =>(6-1)!
16.In how many ways can 5 ladies and 5
gentlemen be seated at a round tables .so that no
two ladies are seated together?
GM5 L5 gM1
L4
L1
GM4
GM2
L3
GM 3 L2
4!*5!
