Question

Find the no. of arrangements of the letters in the word PENCILS if a) e preceeds i and b) there are three letters between e and i

Answer 1

(a) I think 120, though I am not good at these types of questions

Answer 2

abdul could you please show how you got your answ thx!

Answer 3

I don't believe myself. Let joemath too post the answer, let's see if I am right.

Answer 4

The second one is easier to explain. There are only 6 possibilities concerning the E and I.

E___I__
I___E__
_E___I_
_I___E_
__E___I
__I___E

Pick one. Now we have 5 remaining letters to put in the other places. The number of ways we can do that is 5! = 120. So 120 ways for the 5 letters * 6 ways for the E and I gives 720 total combinations.

Answer 5

For the E preceeding the I, again, looking at just E and I we get:

EI_____
E_I____
E__I___
E___I__
E____I_
E_____I
_EI____
_E_I___
...
so on and so forth. If you count them all, we get 21 ways (again, just looking at the E and I). Again, pick one of them. Now we look at the remaining letters. There are 5, and the total number of ways to arrange 5 things is 5! = 120. So 120* 21 = 2520

Answer 6

Oh, I thought E just precedes I.
Sorry

Answer 7

Good explanation Joemath :)

Answer 8

thank you abdul and joemath. however joemath may i ask whether there is a more efficient way of finding out there are 21ways other than drawing it out?