Question

What is the probability arranging the
letters of the world ENGLISH" so that
the vowels never be separated.​

Answer 1

Answer:

Step-by-step explanation:

The word 'VICTORY' contains 7 different letters.

Total number of ways in which these letters can be arranged, N = 7 !

Number of ways in which these letters can be arranged such that no vowel come together, N(E) = Total number of ways - Number of words in which vowels come together.

Now, to calculate the number of words in which vowels come together, we take the vowels I and E together and treat them as one letter.

Then, the letters to be arranged are VCTRY(IO).

These 6 letters can be arranged in 6 ! ways.

Also, the vowels in the group (IO) can be arranged amongst themselves in 2 ways.

Number of words in which vowels come together = 6 !*2

Thus, N(E) = 7 ! - 6 !*2

Hence, required probability = N(E)N = 7!−6!×27! = 57

Answer 2

Answer:

6!

Step-by-step explanation:

vowels are EI

6! is the answer