Question

number of ways of selection of $4$ letter from word "IITJEE" is.

Answer 1

Lets just group them first:

(II)TJ(EE)

So Different ways would be:

1. All different words are been used

ITJE

No. Of ways =4!= 4x3x2=24

2. Two different and two similar words are used

a) IITJ

b) EETJ

c) IITE

d) EETI

e) IIJE

f) EEJI

(4! ÷2!)×6=12×6=72

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

3. Two similar, two similar

IIEE

No of ways=4!÷(2!2!)=3×2=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