permutations and combinations question from fitzy (1 Viewer)

[h3ll h0und]

i really suck at permutations and combinations nd i cant do this question:

How many arrangements can be made by the letters of the word definition

(i) if the letters 'i' do not occupy the first or last place
(ii) if the letters 'i' are together?

can someone pls explain?
thnx in advance

 

[5647382910]

i) there are 10 spots to fill:
Remember always do ur restrictions first: since the three i's cant be in the first spot there are only 7 letters that can, and for the last spot there are 6 since one has been used up in the first spot. in the second spot there are 8 letters that can fill since we can now use the i's, and then 7 for the next, 6 then 5 etc
giving: 7 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 x 6; but since some of the objects are alike we divide by 3! x 2! since there are 3 i's and 2 n's.... this gives 141120
ii) consider the 3 i's as one letter: there are 8! arrangments and since weve made the three i's one object we dont need to divide by 3! only by 2! for the 2 n's. This gives 8!/2! which gives 20160

hope that helps

 

[h3ll h0und]

k i get it thnx