The Hawaiian alphabet (known as piapa) was first written by 19th century mission

Question

The Hawaiian alphabet (known as piapa) was first written by 19th century missionaries and consists of 12 letter; A,E,I,O, and U, and the consonants H,K,L,M,N,P, and W. Assuming all possible arrangements of these letters could be words:

a) What is the maximum possible number of 8- letter words?

b) How many 7- letter words can start with an H, end with an I, and contain no P's?

c) How many distinct arrangements are there of the letters in PUAHAIKUAHU?

d) What is the maximum possible number of 9-letter words in which no letters are repeated?

Explanation / Answer

a)total number of 8 letters word to choose from 12 letters =128 =

b)here in that word we need to select middle 5 letters for which we have 11 choices hence number of words =115

=161051

c) total there are 1 P, 3 U, 3 A, 2 H, one I, One K , 11 letters

hence number of words =11!/(1!*3!*3!*2!*1!*1!)=554400

d)maximum possible number of 9-letter words in which no letters are repeated =(11)9 =11!/2! =19958400

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