Question

Number of 4 letter words that can be formed with the letters of the word IIT JEE is:

• A. $42$
• B. $82$
• C. $102$
• D. $142$

Answer 1

Answer: (C)

$102$

Case-$I$ All different:

In the word $IITJEE$ the letters $I$ and $E$ are repeating twice.

Thus, the different letters are $I$, $T$, $J$ and $E$.

The first letter can be filled in $4$ different ways.

The second letter can be filled in $3$ different ways.

The third letter can be filled in $2$ different ways.

The fourth letter can be filled in one way.

Thus, the total number of arrangements equals $4\times 3\times 2\times 1=24$

Case$II$ Two Similar, two different

$a)IITJ$

$b)EETJ$

$c)IITE$

$d)EETI$

$e)IIJE$

$f)EEJI$

$\left(\frac{4!}{2!}\right)\times 6=12\times 6=72$

(Its divided by $2!$ because there are two similar letters)

Case$III$ Two Similar,Two similar

$IIEE$

No of ways$=\frac{4!}{(2!2!)}=3\times 2=6$

(Its divided by $2!2!$ because there are two sets of similar letters)

Adding all of them, $24+72+6=102$

$\therefore$, there are $102$ four-letter words formed from $IITJEE$