Dear math experts, I hope this finds you well.

I solved 2 questions and I wonder whether my answers are correct.

1) A coach must choose 8 players randomly from 10 players and assign them to three different cars to transport them to an out-of-town game: 2 in car A, 3 in car B, and 3 in car C. In how many ways can this be done?

In this case, we are choosing people randomly, therefore do we need to use combination and divide 10C8 by (2! 3! 3!), to avoid repetition?

2) In how many ways can the letters and numbers of MATH1011 be arranged, if all the letters must be put together?

In this case, we are putting each letter and number together, therefore I think that no repetition is allowed. Hence I think that: 4P4 x (4! / (3! 1!) is the method for this question.

If both methods are wrong, feel free to tell where are my errors and what are correct methods.

Best regards