Answer:
36 non repeating, 72 repeating (AB=BA)
Step-by-step explanation:
There is a theoretical approach to solving this question. We have formulae for such types of question in ‘Permutation and Combination’ chapter but let me solve it through my approach.
There are 9 members in the unit.
we have to choose only 2 people out of them randomly.
let the members be A, B, C, D, E, F, G, H an, I
A can be chosen first with one of the rest as the second person.
Like AB, AC, AD, AE … AI ………………………(1)
by this, we can choose people in 8 ways.
we will also have 8 ways as BA, CA, DA, … IA ………..(2)
the series (2) is completely reverse of series (1)
now perform the same action taking B as first-person and people after B as the second person.
by this, we will have 7 ways
and 7 ways again in reverse mode.
The same process with C, D, E and other members
we get
8*2 = 16 ways with A
7*2 = 14 ways with B
6*2 = 12 ways with C
5*2 = 10 ways with D
4*2 = 8 ways with E
3*2 = 6 ways with F
2*2 = 4 ways with G
1*2 = 2 ways with H
and I can not be selected lonely because there is no person after I.
SO total ways = 16 + 14 +12 + 10 + 8 + 6 + 4 + 2 = 72 ways
72 will be the answer if the selection of A first and B second is different from the selection of B first and A second.
If AB = BA then the answer will be 72/2 = 36
(It is my approach and easier way for me than the traditional formulae)
