The Hawaiian alphabet (known as the piapa) was first written by 19 th century mi
ID: 3132760 • Letter: T
Question
The Hawaiian alphabet (known as the piapa) was first written by 19th century missionaries and consists of 12 letters; the vowels A, E, I, O, and U, and the consonants H, K, L, M, N, P, and W. Assuming that all possible arrangements of these letters could be words:
a) What is the maximum possible number of 4-letter words?
b) What is the maximum possible number of 7-letter words in which no letters are repeated?
c) How many 8-letter words can start with a P, end with an A, and contain no U’s?
d) How many distinct arrangements are there of the letters in KOLAUKALAKI?
Explanation / Answer
Given,
Total number of alphabets in the language =12
A,E,I,O,U and consonants H,K,L,M,N,P,W
a) maximum possible number of 4-letter words
WIth repetition, 12*12*12*12= 20736
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b)maximum possible number of 7-letter words in which no letters are repeated
=12 P 7
=12*11*10*9*8*7*6
=3991680
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c) No of 8-letter words can start with a P, end with an A, and contain no U’s
so, remaining 6 places are to be filled with 11 alphabets
repetition allowed = 11^6 = 1771561
repetition not allowed = 11 P 6 = 332640
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d) No of distinct arrangements are there of the letters in KOLAUKALAKI
The given word conatins 11 letters, K -3 times, A- 3 times, L- 2, O-1,u-1,I-1
No of arrangements
11!/ (3! * 3! * 2!)
= 554400
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