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

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626

1422

1200

1340

answer is B.

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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.

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