# Do you like Mathematics?

@archana_aucsse (100)

India

May 18, 2007 10:29am CST

My favourite subject is mathematics.
If you are interested solve the following problem and send me a reply or discuss on the same on the forum.
"DEFEATED" is word.
Calculate the number of possible words which does not contains any of the two E's together??

1 response

@josephperera (2916)

• Sri Lanka

21 May 07

I can remember working out sums like this under the subjec "Permutations and Combinations" about 30 years ago in school. I'll try my best, but I am eagerly waiting for the correct solution.
This is an 8 letter word. It has 3 Es. But there is a limitation regarding E. So we will forget it and think of this as a 5 letter word.
The number of words you can make with 5 letters is, 5x4x3x2x1. This works out to 120. But the D repeating two times brings this down by half. So the numebr of words are 60.
Now lets take one 5 letter words. It has 6 spots to insert another letter without touching each other. So in how many ways can we put 3 Es into these 6 spots. I think it is 6x5x4/3x2. That is 20.
So altogether there are (60 x 20) 1200 possibilities.