Answer:

There are 10 competitors, and mary must choose 3 crowned winners. Also, she must designate 1 of them as a grand winner.

Now, 10 competitors are present, and the teacher has to choose 3 as winners.

Let the competitors be A, B, C, D, E, F, G, H, I, J.

There are numerous patters:

A, B, C; B, C, D; C, D, E; D, E, F; E, F, G; F, G, H; G, H, I; H, I, J, J, A, B; J, B, C, and this goes on.

Here, we can use permutations.

So, 10 competitors can be written as 10! which equals to

3628800.

But, only 3 winners should be chosen:

Using n!/(n-r)! :

3628800/(10 - 3)! = 3628800/5040 = 720.

And she designated 1 grand winner.

There are 3 winners, and there will be 1 grand winner.

Then, there are only 3 ways where she can select a grand winner.

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