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

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 6-letter words?

b) How many 7-letter words can start with a W, end with an A, and contain no O’s?

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

d) What is the maximum possible number of 8-letter words in which no letters are repeated?

Explanation / Answer

Please Note nPr = n!/(n-r)!

Total Letters is 5 Vowels + 7 Consonants = 12

a) 6 letter words ( with repetition) = 12 * 12 * 12 * 12 * 12 * 12 = 126.

b) Here 2 positions, that is the 1st and the last place is fixed. There are 5 places remaining, and any 11 letters (excluding O can be placed here). Therefore 11 * 11 * 11 * 11 * 11 = 115.

c) PAPAHAWANUI - This has a total of 11 letters in which we have 4 A's and 2 P's. Therefore Distince Arrangements = 11! / (4!*2!) = 831600

d) 8 letter words without repetition.

12P4 = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 = 19958400

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.