Question

number of ways in which we can arrange FANTASTIC that vowels come next to each other​

Answer 1

Explanation:

it cannot come according to my perception

Answer 2

Answer: The answer is 7560

The number of ways in which we can arrange FANTASTIC that vowels come next to each other​ is 7560.

Explanation:

• The given word is FANTASTIC
• All the consonant FNTSTC = 6
• All the vowel in the word are AAI = 3
• Total number of alphabet in the word are 9.
• Considering all the three vowels as 1 alphabet
• Number of ways in which all 3 vowels can be arranged = $^3C_2$
• $^3C_2=3$
• All consonant and vowels(taken together) combine to form a word series of 7 words
• Number of ways these 7 can be arranged without repetition $= \frac{7!}{2!}$$\frac{7!}{2!} = 2520$
• Total Number of ways FANTASTIC can be arranged  so that all the vowels come next to each other are = 3 X 2520 = 7560.

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