Answer :

We have, 6 objects {B}, {H}, {A}, {R}, {A}, {T} and there are 2 A's.


So, the words can be formed out of the letters of the word ‘BHARAT’ taking 3 at a time can be done in 2 ways:


Case-1: When all the letters are distinct.


We have, 5 distinct letters, out of which taking three at a time, the number of words that can be formed = 5P3




= 60


Case-2: When 2 A’s are selected.


So, we have, 2A’s and 1 letter is to selected out of the 4 distinct letters, which can be done in = 4P1




= 4 ways.


Now, the 3 letters can be arranged among themselves, but there are 2 A’s, so the number of ways in which arrangement can be done is




So, in this case, total number of words that can be formed


= 12.


The number of arrangements of the letters of the word BHARAT taking 3 at a time is = (60 + 12)


= 72.

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