ncert cbse 11th maths excercise 7..3 chapter 7
exercise 7.3
11.In how many ways can the letters of the word PERMUTATIONS be arranged if
i)words start with P and end with S
ii)vowels are all together
iii)there are always 4 letters between P and S
There are 12 letters in the word PERMUTATIONS
i)words start with P and end with S
If the word start with P and end with S
first slot and 12th slot can be filled in 1 way each.
After removing P and S,
For the remaining 10 slots there are 10 items
with 2 T's,
So number of words starting with P and end with S
= 1 *[(10!)/(2!)]*1 = 1814400
ii)vowels are all together
vowels in the given word are E,U,A,I,O
If the vowels are together, think of the 5 vowels as a single block.
Inside the block the vowels can be arranged in (5!) ways
Now this block of vowels with the remaining 7 consonants
make up 7+1=8 pieces with 2 T's
which can be arranged in [(8!)/(2!)] ways
Number of words in which the vowels are together = (5!)*[(8!)/(2!)]
=120*20160=2419200
iii)there are always 4 letters between P and S
When there are 4 letters between P and S
one particular arrangement will be
P x x x x S # # # #
in this example first and fifth slots can be filled in 1 way each
and the remaining 10 slots can be filled with 10 remaining letters
containing 2 T's in = 1 *[(10!)/(2!)]*1 = 1814400 ways
Now possible re-arrangements are
1 P x x x x S # # # ###
2 #P x x x x S # # # ##
3 ##P x x x x S # # ##
4 ###P x x x x S # ##
5 ####P x x x x S##
6 #####P x x x x S#
7 ######P x x x x S
Now the position of P and S can be interchanged
8 S x x x x P # # # ###
9 #S x x x x P # # # ##
10 ##S x x x x P # # ##
11 ###S x x x x P # ##
12 ####S x x x x P##
13 #####S x x x x P#
14 ######Sx x x x P
A total of 14 arrangements
number of words where
there are always 4 letters between P and S
=1814400*14
=25401600
ncert cbse 11th mathematics chapter 7 permutations exercise 7.3
11.In how many ways can the letters of the word PERMUTATIONS be arranged if
i)words start with P and end with S
ii)vowels are all together
iii)there are always 4 letters between P and S
ncert cbse 11th mathematics chapter 7 permutations miscellaneous exercise
1.How many words each of 2 vowels and 3 consonants can be formed using the letters of the word DAUGHTER
2. How many words of can be formed using all the letters of the word
EQUATION so that the vowels and consonants occur together?
4. If the different permutations of the word EXAMINATION are arranged in
a dictionary how many words are there in this list before the first
word starting with E
solutionThere is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work. Your internet usage may be tracked by the advertising networks using tracking cookies
No comments:
Post a Comment
please leave your comments