ncert cbse 11th maths excercise 7.3 chapter 7

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

solution

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

solution

2. How many words of can be formed using all the letters of the word

 EQUATION  so that the vowels and consonants occur together?

solution

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

solution

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