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
(A) 120
(B) 360
(C) 720
(D)2880
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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 I I E
- 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 5 C 4. Also the consonants are placed in 4! Ways.
- So we have 4! x 5 C 4 x 4! Ways
- So we get 4 x 3 x 2 x 1 x 5! / 4! (5 – 4)! X 4!
- 24 x 5 x 4 x 3 x 2 x 1
- = 2880 ways
Reference link will be
https://brainly.in/question/12119981
Answered by
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Answer:
2880ways hope it helps you
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