Using all the letters of the word PROBLEM how many words can be formed such that the consonants occupy the middle place ?

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Solution

here the consoanant letters are P,R,B,L,M
AND IT SHOULD BE LOCATE AT CENTRES ,SO WE CAN FIX THE VOWELS
that is we fix the letters E and O at extreme ends
there are 7 letters when we fix o at left and E at extreme right
then the possible numbers =5!4!3!2!1!
=34560
in addition to this there is a possiblity of fixing O ast the LEFT and E at right
there for all possible number of ways = 2*34560
=69120

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