The number of ways of forming an arrangement of 4 letters from the letters of the word “IITJEE”?

15

Hi Akhil,

We have to consider cases here.

1. All four letters different. in this case we have to arrange from ITJE

This will give rise to 4! arrangements = 24

2. Two alike, two different.

Possibility IITJ (12 arrangements), TJEE (again 12 arrangements). Total 24 in this case.

3. Two alike of one kind, two alike of another kind.

Possibility is from IIEE [total 4!/(2!*2!) = 6 arrangements)

So in all there can be 24+24+6 = 54 possible arrangements of 4 letters from IITJEE.

That would be the answer. Hope it helps.

Regards,

Ashwin (IIT Madras).

thank you! but the answer was 102! could you please tell me how to get it. OR is your answer correct?

Hi Akhil,

Extremely sorry. If you note in the 2nd case, i had missed some cases.

For the case of 2 alike and 2 different - possibilities would be:

IITJ, IITE, IIJE, EEIT, EEIJ, EETJ. Each will give 12 arrangements. So the 2nd case will have a total of 12*6 = 72 arrangements.

Hence total number of ways = 24+72+6 = 102 ways.

Thanks for mentioning that. And sorry for the error.

Regards,

Ashwin (IIT Madras).