Question

The letters of the word ‘MEDICINE’ are arranged in such a way that no two consonants are together. The number of ways this can be

Answer 1

Answer:

the no. of ways by this can be done is = 5!*4!/2!

note in this case the question says that no two consonants are together and this case is entirely different from the one in which the question says all the consonants are never together

Answer 2

Answer:The number of ways this can be 2880 ways .

Step-by-step explanation:

Given the letter of the word (MEDICINE) are arranged in such a way that no two consonants are together .The number of ways this can be

• We need to find the number of ways that can be arranged so that no two consonants are together.
• Now we have the vowels placed as E | | E
• Now we have the 4 vowels that can be placed in distinct points in 4! Ways.
• Now we have the 4 vowels that can be placed in distinct points in 4! ways.
• Now no two consonants are to be together. Now we can place the consonants in between the vowels (alternate) and no consonant can come together.
• Now there are 4 consonants but there are 5 places and 4 places are perfectly fit and one place is left vacant. So selecting 4 places out of 5 we have 5C4.Also the consonants are placed in 4! Ways.
• So we have 4!×5C4×4! Ways
• So we get 4×3×2×1×5!/4!(5-4)!×4!
• =  24×5×4×3×2×1=2880 ways