Find the number of ways in which the letters of word 'MEDICAL' be arranged if A and E are together but all the vowels never come together.




Updated On: 24-5-2021


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Answer :
Solution :
We have letters M,D,C,I,E,I,A <br> Let us first arrange vowels, which has number of ways 4!. <br> Five places are created marked as `xx`. <br> `xx M xx Dxx CxxL xx` <br> In these five places, we have to arrange vowels A, E, I so that A and E are together but all are not together. <br> So, we have to arrange AE and I. <br> Number of ways are `.^(5)C_(2)xx2!xx2!` (as also be arranged in 2! ways) <br> So, total number of arrangements `=4!xx .^(5)C_(2)xx2!xx2=960`



00:00 - 00:59hello friends the question is find the number of ways in which the letter of word medical be arranged if A and B are together but all the vowels never come together given that we have word medical so total letters are 7 so we can see it as 75 to real so let's assume we have a box of 7 letters so 1 2 3 4 5 6 and 7 2 in 7 letters condition is given that A and E
01:00 - 01:59I together so let's take this case even with all vowels are together or not so we can say agro1 ki band box swamini boxes are left 3 4 5 and 6 1 box so 23456 is left so we have two to six ways so number of ways 6 factorial and have two ways of interchanging so we can write to factorial so that will be 1440 now we have another
02:00 - 02:59addition there all the walls were all the vowels are never together in that case a e i all three are vowels now if these three are together then we have to subtracted from total days so taking a e combine how many boxes 1234 12345 total total vowels a e i that is 5 factorial into these three can also interchange in them so how many ways three ways so 3 factorial
03:00 - 03:59get 5 factorial is what 120 in 26 that is 7:20 so now total required ways that is 1440 - 720 that will be 720 so 720 answer thank you

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