What is the rank of RANK ????
In a certain dictionary words with only letters R,A,N,K are given . What is the rank of RANK in this dictionary
DETAILS......... Words though meaning less or composed of only 1 letter are also mentioned in this dictionary
[This question is not clearly phrased.]
The answer is 54.
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1 solution
I am not well familiar with combinatorics but knows formulae for Permutation with which I have solved the problem. A confusion that may arise is, should the words formed by repetition of letters R, A, N, K be counted in. But the right answer is obtained only when those aren’t included. So let us look at the rest:
All words starting from A, K, and N should be counted in, as they all occur before RANK in the dict. • When taken in sets of 1: Permutation: 4P1 = 4 No.of words = 4 {R, A, N, K}
• When taken in pairs of 2: Permutation: 4P2 = 12 No.of words = 10 { excluding RN, RK }
• When taken in sets of 3: Permutation: 4P3 = 24 No.of words = 20 { excluding RKA, RKN, RNK, RNA}
• When taken in sets of 4: No.of words starting with A, K, N = 18. No.of words starting with R = 2. Explanation: Words counted in: All words with 4 letters starting with A, N, & K ( excluding repetition of letters from all), and words starting with R, which has 2nd and 3rd letters in the order AN & AK. Therefore, total no.of word: 4 + 10 + 20 + 18 + 2 = 54. THANK YOU... Hope you get it.