## lirffej 2 years ago how many different words can be formed from the word COMPLETE?..

1. sauravshakya

8!/2!

2. lirffej

what are those words??..can you explain why come up of that solution?

3. sauravshakya

n! = n*(n-1)*(n-2)*...*3*2*1

4. ZeHanz

There are 8 letters. To make words, you put the letters down, one by one. The first one can be chosen in 8 ways. The second in 7 ways. You've got 8*7 =56 possibilities already! This continues all the way down to the last letter. So you have 8*7*6*5*4*3*2*1 possibilities. The mathematical notation for this is 8!

5. ZeHanz

One problem to solve: there are 2 E's so we have counted too much. We have to divide by the number of same possibilities if the two E's are switched. This switching of E's can be done in 2*1 = 2! ways. End result: 8!/2! = 20160

6. lirffej

are you sure of that??

7. ZeHanz

Surprising many, isnt it?

8. lirffej

@ZeHanz are you sure??

9. ZeHanz

Sure I'm sure!

10. ZeHanz

If you read carefully what I wrote, you'll come to the same conclusion. There is no escape. There are surprisingly many ways to make words with 8 letters...

11. lirffej

20160 words??

12. ZeHanz

Of course, most words would be difficult to pronounce and without meaning. Nevertheless, there are 20160 possibilities, If you find that hard to grasp, just try with fewer letters: If you have 1 letter, you can make only one "word". With 2 letters, the firat one can be chosen from 2, the second has only one possibility. So: 2*1 3 letters: 3*2*1 = 6 4: 4*3*2*1 = 24 It goes up really fast!

13. lirffej

ok..thanks,now i understand..

14. ZeHanz

YW!