Q. 18

# Mark the correct alternative in the following:The number of arrangements of the letters of the word BHARAT taking 3 at a time isA. 72B. 120C. 14D. none of these.

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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