Question

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

Answer 1

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

Answer 2

Answer:

2880ways hope it helps you