Two-step experiment question

[britnium]

Hello.

I am having trouble with the following questions:

'The 10 students who completed a special flying course are waiting to see if they will be awarded the one Distinction or the one Merit award for their efforts.
a) In how many ways can the two awards be given if:
i) the same student can receive both awards?
I originally got 100 outcomes which my math teacher said was correct, but I don't know why it should be 100. My math teacher instructed me to multiply the 10 students by 10, but I am unsure of where she got the other 10 from.
ii) the same student cannot receive both awards?

 

[MarkFL]

For both these problems, I would use the fundamental counting principle.

i) For the first award, there are 10 students from which to choose, and because the same student may receive both awards, for the second award we also have 10 students from which to choose, and so the number \(N\) of ways the two awards could be given is:

[MATH]N=10\cdot10=100[/MATH]
ii) Can you apply the same principle here?