MATHS Permutation

Answer: 3360

Solutions:

for the case of 0 "i" is chosen,
the question become choose 4 letters out of 8 different letters
thus there are 8P4 arrangements

for the case of 1 "i" is chosen,
the question become choose 1 "i" and 3 "not i" out of 8 different letters
thus there are 8C3 x 4P4 arrangements

for the case of 2 "i" are chosen,
the question become choose 2 "i" and 2 "not i" out of 8 different letters
thus there are 8C2 x 4P4 / 2P2 arrangements where 2P2 means repeated "i"

therefore, the total arrangements
= 8P4 + 8C3 x 4P4 + 8C2 x 4P4 / 2P2
= 1680 + 1344 + 336
= 3360

"DICTIONARY" has 10 letters.
Number of arrangements
=10P4
=5040

2012-08-29 18:21:48 補充：
Do you mean 4 DIFFERENT letters?
If so, number of arrangements
=9P4
=3024
Next time, you should clarify whether the letters can be repeated, or the answer will be different.
NOTE:choosing 2 'i's from 'dictionary' = choosing any two letters