Home
Class 12
MATHS
The number of different words that can b...

The number of different words that can be formed using all the letters of the word 'SHASHANK' such that in any word the vowels are separated by atleast two consonants, is

A

`2700`

B

`1800`

C

`900`

D

`600`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` The letters other than vowels are `SHSHNK` which can be arranged in `(6!)/(2!2!)` ways.
Now in its each case, let the first `A` be placed in the `r^(th)` gap. Then the number of ways to place the `2nd A` will be `(7-r-1)`. So, the total number of ways `=(6!)/(2!2!)sum_(r=1)^(5)(6-r)`
`=(6!)/(2!2!)xx(5+4+3+2+1)`
`=2700`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|2 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Matching Column Type|1 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE PUBLICATION|Exercise Sovled Examples|22 Videos

Similar Questions

Explore conceptually related problems

The number of words that can be written using all the letters of the word IRRATIONAL is -

How many different words can be formed with the letters of the word "MATHEMATICS"

Find the number of different words that can be formed using all the letters of the word DEEPMALA if two vowels are together and the other two are also together but separated from the first two.

Number of words of 4 letters that can be formed with the letters of the word IITJEE is

How many different words can be formed with the letters of the word ORDINATE so that beginning with O

Number of nine-lettered word that can be formed using all the letters of the word 'MEENANSHU' if alike letters are never adjacent is

How many words can be formed from the letters of the word COMMITTEE?

How many different permutations can be made by taking all the letters of the word BENGALI?

Find the number of seven letter words that can be formed by using the letters of the word SUCCESS so that the two C are together but no two S are together.

How many different words can be formed with the letters of the word ORDINATE so that two vowels occupy odd places