How many words can be formed from the letters of the word ordinate so that vowels occupy odd places ?`?

Text Solution

Solution : The given word consists of 8 letters, out of which there arr 4 vowels and 4 consonants. <br> Let us mark out the positions to be filled up, as shown below: <br> `(""^(1))(""^(2))(""^(3))(""^(4))(""^(5))(""^(6))(""^(7))(""^(8)).` <br> Since vowels occupy odd places, they may be placed at 1, 2, 3, 5, 7. <br> Number of ways of arranging 4 vowels at 4 odd places <br> `= ""^(4)P_(4)=4! =24.` <br> The remaining 4 letters of the given word are consonants, which can be arranged at 4 even places marked 2, 4, 6, 8. <br> Number of ways of arranging 4 consonants at 4 even places <br> `= ""^(4)P_(4)=4! =24.` <br> Hence, the total number of words in which the vowels occupy odd places `=(24xx24) =576.`

How many words can be formed with the letters of the word "ORDINATE" so that vowels occupy odd places? And sir/mam can this be done like this:No. Of words that can be formed =4 ! * 3 ! * 2 !

Open in App