The number of ways in which the letters of word MEDICAL can be arranged such that A and E are together but all the vowels never come together is .

Question

The number of ways in which the letters of word MEDICAL can be arranged such that A and E are together but all the vowels never come together is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

We have letters M , D , C , L , E , I , A We have 4 consonants, which can be arranged in 4 ! ways. Now, there are five places, where we have to arrange vowels A , E , I so that A and E are together but all are not together. So, we have to arrange AE and I. Number of ways are 5 C2 × 2 ! × 2 ! (as AE can also be arranged in 2 ! ways) So, total number of arrangements =4 ! × 5 C2 × 2 ! × 2 ! = 960

Q. The number of ways in which the letters of word MEDICAL can be arranged such that A and E are together but all the vowels never come together is ____.

Q. The number of ways in which the letters of word MEDICAL can be arranged such that $A$ and $E$ are together but all the vowels never come together is ____.