Question

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 at least 2 consonants is

Answer 1

2700 is the correct answer
It's of PnC

Answer 2

Answer:

2700 is the required number of  different words that can be formed

Step-by-step explanation:

Explanation:

Given , a word Shashank  .

Here , we can see that there are two vowels in the word and both letters are A . And in the word there are two S , two A and two H letters .

Step 1:

Therefore , total number of different words = $\frac{8!}{2! 2!}$ = 5040 .

Here , we take both A together so total no. of digit we have 7 .

Now , number of ways of different words where both A  are together= $\frac{7!}{2!2!}$

=  1260 .

And Number of ways in which there is exactly one constant between A  = $\frac{6!}{2!2!}$ = 180  × 6 = 1080 .

Therefore , the number of words the vowel A  is separated at least two constant = 5040 - (1080 + 1260) = 2700.

Final answer:

Hence , there are 2700  words in which at least two constant are  there between vowels .

#SPJ3