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If all the letters of the word AGAIN be arranged as in a dictionary,what is the fiftieth word?A. NAAGIB. NAAIGC. NIAAGD. NAIAG |
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Answer» In dictionary the words at each stage are arranging the other four letters GAIN, we obtain 4!=24 words. Thus, there 24 words which start with A. These are the first 24 words. Then, starting with G, and arranging the other four letters A, A, I, N in different ways, we obtain `(4!)/(2!)=(24)/(2)=12` words. Thus, there are 12 words, which start with G. Now, we start with I. the remaining 4 letters A, G, A, N can be arranged in `(4!)/(4!)=12` ways. So, there are 12 words, which start with I, Thus, we have so far constructed 48 words. The 49th word is NAAGI and hence the 50th word is NAAIG. |
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