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BITSAT 2010
Exam
BITSAT
Year
2010
Subject
Mathematics
Chapter
Binomial Theorem

BITSAT 2010 · Mathematics · Binomial Theorem

With 17 consonants and 5 vowels the number of words of four letters...

With 17 consonants and 5 vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end is

Options

  1. A5780
  2. B2890
  3. C5440
  4. D2720

Correct answer

A. 5780

Step-by-step solution

The two letters, the first and the last of the four lettered word can be chosen in (17)2(17)^2 ways, as repetition is allowed for consonants. The two vowels in the middle are distinct so that the number of ways of filling up the two places is ({ }^5 P2=\mathrm{P}_{2}=20). The no. of different words (=(17)^2 \cdot20=5780).
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