'' DICTIONARY" ?
更新1:
BUT choosing 4 letters out of this word ......
更新2:
but the word D I C T I O N A R Y has 2 letters of " I " Some words will repeated with this counting.
MATHS Permutation
2012-08-29 1:39 am
How many different arrangements are there in choosing 4 letters out of
'' DICTIONARY" ?
'' DICTIONARY" ?
回答 (2)
2012-08-31 5:51 pm
✔ 最佳答案
Answer: 3360Solutions:
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
參考: knowledge
2012-08-29 3:58 am
"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
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
參考: me, me
收錄日期: 2021-04-20 13:17:26
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120828000051KK00658