How many four-letter words can be formed using the letter “INEFFECTIVE”?

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

626

1422

1200

1340

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The word “INEFFECTIVE” contains 3 Es, 2 Is and 2 Fs, and 1 N, C, T, and V.
That implies we have 7 different kinds of letters out of which we have to select 4 letters.
possible ways are given by permutations of 4 letters out of the given 7.

P_{4}^{7} = 840

two same letters and remaining both different letters =

C_{2}^{3} \times C_{2}^{6} \times P_{2}^{4} = 540

two same letters of each kind =

C_{2}^{4} \times C_{2}^{3} = 18

three letters of the same kind and one of the different =

C_{1}^{1} \times C_{1}^{6} \times C_{3}^{4} = 24

Total number of ways
⇒ 840 + 540 + 18 + 24 = 1422
So, Option 2 is correct.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th