Question
Download Solution PDFUsing all the letters K, N, A, G and A, 5 letter words are made (with or without meaning). If these words are arranged as in a dictionary, the word NAAKG will appear at what place?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Letters = K, N, A, G, A
Word to find position = NAAKG
Calculation:
Arranging letters in alphabetical order: A, A, G, K, N
Words starting with A:
Number of arrangements = \(\frac{4!}{1!}\) = 4 × 3 × 2 × 1 = 24
Words starting with G:
Number of arrangements = \(\frac{4!}{2!}\) = 12
Words starting with K:
Number of arrangements = \(\frac{4!}{2!}\) = 12
Words starting with N:
Words starting with NA:
Words starting with NAA:
Number of arrangements of K, G = 2! = 2 × 1 = 2 (NAAGK, NAAKG)
Position of NAAKG = (Words starting with A) + (Words starting with G) + (Words starting with K) + 2
⇒ Position of NAAKG = 24 + 12 + 12 + 2
⇒ Position of NAAKG = 24 + 12 + 12 + 2
⇒ Position of NAAKG = 50
The word NAAKG will appear at the 50th place.
Last updated on Dec 9, 2024
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