There are 12 steamers playing between A and B. In how many ways could the round trip from A be made if the return was made on
A.The same steamer?
B.The different steamer?

Hint: For the first part as it is given we have to return from the same steamer so we just have to choose once, when we are going from A to B, for the return trip it will be the same. And for the second part we have to again choose from the ones that are left then we have to multiply it with the number that we have chosen from A to B.

Complete step-by-step answer:
Let’s first solve (a),
For (a):
The total number of possible choices from A to B is 12. And from B to A we will take the same one hence from B to A is 1.
Total case = $12\times 1=12$
Let’s first solve (b),
For (b):
The total number of possible choices from A to B is 12. And from B to A we will take the different one that we have taken from A to B, hence from B to A the possible option is 12 – 1 = 11.
Total case = $12\times 11=132$
Hence, we have found all the cases for the round trip from A to B.

Note:One can also solve this question by taking from B to A then again from A to B. And then we can apply the same process for the same steamer and then the different steamer, the answer will be the same in both the process.