permutations help (1 Viewer)

[mannnnndy]

ok can someone please explain permutations 2 me. i know its supposed 2 b easy but i must b really dumb or something cause it hasnt really clicked with me. i sorta get it 4 the most part but for some things i dont really get why u do something. like in this question,
how many ways can the letters of the word SCIENCE be arranged if
a)the two C's are together
b) the letters I & N are together
c) there are 3 letters between the C's
so if someone could pleaze explain how 2 do these questions and WHY u do the things in the steps i would very much appreciate it. thanx

 

[Lazarus]

(a)

Treat the two Cs as a single letter (because they will always be together). There are then 6 letters so the total number of possible permutations will be 6! = 720. As there are two identical Es, however, you must also divide by 2!. The final number of permutations is 6! / 2! = 360.

(b)

Treat the I and N group as a single letter. There are then 6 letters. There are 6! = 720 possible permutations, but in this case, the I and N can be switched around inside their little group, so the total number of permutations is 6! * 2! = 1440. As there are two identical Es and two identical Cs, however, you must also divide twice by 2!. The final number of permutations is (6! * 2!) / 2!2! = 360.

(c)

Possible situations for having three letters between the Cs:
C***C**
*C***C*
**C***C
In each case, the other letters can be arranged 5! = 120 different ways. But there are 3 situations, so the total number of permutations is 3 * 5! = 360. As there are two identical Es, however, you must divide by 2!. The final number of permutations is (3 * 5!) / 2! = 180.

 

[mannnnndy]

what about the letters that r the same like the C's and E's? dont u have 2 divide or something with them?

 

[Lazarus]

Sorry, I forgot about that - it's been a while. I've edited my post above to take into account the identical letters.

 

[mannnnndy]

thanx so much 4 ur help i really needed that, specially since my 3u trials r in 4 days and i dont know how 2 do stuff