Why are there only 12 letters in the hawaiian alphabet
Asked by admin @ in Mathematics viewed by 251 People
The hawaiian alphabet has 12 letters. How many permutations are possible for five of these letters
Asked by admin @ in Mathematics viewed by 251 People
The hawaiian alphabet has 12 letters. How many permutations are possible for five of these letters
Answered by admin @
Answer: The answer is 50980
Step by Step Explanation:
First, temporarily assume that two letters with I are different, call them i 1 and i 2. Three "a" are also called as a 1, a 2 and a 3, and two h as h 1 and h 2. Then there are 11 * 10 * 9 * 8 * 7 = 55440 possible "words" (one of 11 is the first letter, 10 is the second, and so on). But because equal letters do the same "words," some "words" were counted twice or more. We have to deduct the number of "parasitic" counts although it is fairly small. The words that counted more than once are divided into many disjoint sets: 1) with two I but without repetitions of a and h; 2) with two h but without repetitions of a and I 3) with two a but without repetitions of I and h; 4) with three a but without repetitions of I and h; 5) with two I and two a's; 6) two i's and tree a's; 7) two i's and two h's 8) two h's and two a's; 9) two h's and one tree. The first category includes terms counted twice and its scale is (5 * 4) * (6 * 5 * 4) = 2400 (the first I stays at one of the 5 positions, the second at one of the 4, then 11-2i-1h-2a=6). So we have 2400/2 = 1200 to subtract. Group 2 gives -600 as well, and group 3 also. Group 4 gives * (6 * 5) = 1800 (5 * 4 * 3), and the terms are counted 6 times, -300. Groups 5, 7 , 8: 5 * 4 * 3 * 2 * 6 = 720 and counted four times, therefore -180. Group 6 and 9: 5 * 4 * 3 * 2 * 1 = 120, with 12 counts, -10. Altogether -(1200 * 3 + 300 + 180 * 3 + 10 * 2) = -4460.The answer will be 55440-4460 = 50980.
Asked by maham237 @ in Arts viewed by 359 persons
Asked by admin @ in English viewed by 927 persons
Asked by wiki @ in English viewed by 309 persons
Asked by wiki @ in Social Studies viewed by 316 persons
Asked by admin @ in English viewed by 383 persons
Asked by admin @ in Science viewed by 311 persons
Asked by admin @ in Math viewed by 355 persons
Asked by maham237 @ in Mathematics viewed by 295 persons
Asked by maham237 @ in Mathematics viewed by 312 persons
Asked by maham237 @ in Mathematics viewed by 264 persons
Asked by wiki @ in Social Studies viewed by 340 persons
Asked by admin @ in Math viewed by 298 persons
Asked by admin @ in English viewed by 331 persons
Asked by admin @ in Math viewed by 316 persons
Asked by admin @ in English viewed by 269 persons
Asked by maham237 @ in Mathematics viewed by 18206 persons
Asked by admin @ in Mathematics viewed by 8043 persons
Asked by admin @ in Mathematics viewed by 5703 persons
Asked by maham237 @ in Mathematics viewed by 3903 persons
Asked by maham237 @ in Mathematics viewed by 3190 persons
Asked by maham237 @ in Mathematics viewed by 2892 persons
Asked by maham237 @ in Mathematics viewed by 2732 persons
Asked by maham237 @ in Mathematics viewed by 2520 persons
Asked by maham237 @ in Mathematics viewed by 2440 persons
Asked by maham237 @ in Mathematics viewed by 2390 persons
Asked by maham237 @ in Mathematics viewed by 2388 persons
Asked by maham237 @ in Mathematics viewed by 2043 persons
Asked by maham237 @ in Mathematics viewed by 1764 persons