Originally posted by freaking_out
this permutation stuff is driving me nut anyway my question is the following:
find the number of 5 letter words which can be made from the letters of the word HONGKONG.
(the thing thats troubling me is the repetition of some letters)
thanx in advanced
whoa
ok whenever you make words from some but not all of repeated letters such as this, you've got to case bash.
Here we have 5 different letters: H,O,N,G,K
we have pair O,N,G
Notice that you can have 2 pairs at max (since we have 5 letter words).
So:
case1: no repeated letters: 5! = 120
case2: one pair, 3 other different letters: there are 3 types of pairs you can have, each type (e.g. double O), you can internally arrange into combination 5C2, and you have 4 different letters to choose the remaining 3.
thus case2: 3 * (5C2) * 4 * 3 * 2 = 720
case 3: two pairs + 1 different letter: there are 3 'dbl pairs': OONN, OOGG, NNGG. Internal arrangement for each is (5C2)*(3C2) (choose 2 spots from 5 for first pair, choose 2 spots from 3 for second pair), and there are 3 options for the last letter:
thus case3: 3 * (5C2) * (3C2) * 3 = 270
Thus total = 1110
edit: Go Hong Kong!
