Selection of "e" from "e"

Question

Suppose, there are 3 "e" . I want to select 2 e from these 3 e. By common sense, we can say that we can select by only one way...But I want to calculate using combination formula...

MY APPROACH:

During the selection, 2 e will always occur. So, we can calculate excluding 2 e... n∧C_r-2 Where, n=3 and r=2. So, the answer is 1.

Is my approach correct?

Why would you want to use the "combination formula" when it is totally inappropriate to your problem? All 'e's are identical, there is only one way - end of the story! — , Jan 14 '18 at 08:29
Yeah I also know that...But it's that I want to know how can I use it in a formula... — Nehal Samee, Jan 14 '18 at 08:31

score 0 · Accepted Answer · 2018-01-14T08:26:27.717

0

If you want to number all the ways you can choose $k$ elements from a group of $n$ you have to use the binomial coefficient.

In your case the result is: $$\binom{3}{2}=\binom{3}{3-2}=\binom{3}{1}=3$$

But since all the three elements are identical, you have just $1$ way to choose 2 of them. In fact they are undistinguishable.

edited Jan 14 '18 at 08:26

answered Jan 14 '18 at 08:17

How can I choose 2 e from 3 e by 3 ways? – Nehal Samee Jan 14 '18 at 08:19
No matter how you chose, every time it would be only "e"...So, answer should be 1, shouldn't it? – Nehal Samee Jan 14 '18 at 08:21
So, you have a set made of three identical elements? – Jan 14 '18 at 08:21
Yes...All are same... – Nehal Samee Jan 14 '18 at 08:24

Selection of "e" from "e"

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