Question

How many arrangements can be made by the letters of the word DEFINITION a) if the letters i do not occupy the first or last place, (ii) if the letters i are together?

Answer 1

moi do you have any idea how to do this?

Answer 2

LOL i did what you did but according to the solution booklet the answer is not correct. The answer is supposed to be 141, 120. any ideas how they got this???????

Answer 3

You can always write a Python script to answer these types of questions.

Answer 4

for the first one I got 1693440

Answer 5

my answer is wrong though because I'm double counting

Answer 6

yes the answer is supposed to be 141120. hahaha the comma is supposed to make it easier to read. LOL how did you know i was from a different country? hehe

Answer 7

symbol overloading! ah

Answer 8

oh wow i didn't know

Answer 9

definition word has 10 letters
a)_ _ _ _ _ _ _ _ _ _
first and last can't be 'i' so we can use only 7 letters for first ant last place (because we have 3 'i')
7 _ _ _ _ _ _ _ _ _
and for last place only 6 are left
7 _ _ _ _ _ _ _ _ 6
now we can use all letters but 2 letters were already used so again we have 8 letters
7 8 _ _ _ _ _ _ _ 6
now 7
7 8 7 _ _ _ _ _ _ 6
now 6
7 8 7 6 _ _ _ _ _ 6
and until 1
7 8 7 6 5 4 3 2 1 6
and you need to multiply all those numbers
but we have repeated letters: 'i' is repeated 3 times and 'n' is repeated 2 times, so we count them once than more.
to avoid this we need to divide answer by 3!=6 (because 'i' is repeated 3 times) and 2!=2 (because 'n' is repeated 2 times)
so answer is 7*8*7*6*5*4*3*2*1*6/6/2

Answer 10

b) we can group two 'i' letters as one as we would have II D E F I N T O N
so now we have 9 spaces
and it would be just
9*8*7*6*5*4*3*2*1
but we again double counted however this time only letter N is double counted so we need to divide by 2!=2
and answer is 9*8*7*6*5*4*3*2*1/2=181440

Answer 11

is it correct answer? :D

Answer 12

i don't think so