Can someone tell me if this is correct?

four American, three Italians and three Germans are seated at random in a row. what is the probability that 1) those of the same nationality are seated together? 2)Germans are seated together and non-German are seated together

solution:

sample space 10!

1)3!4!3!3!/10!

2)2!4!3!3!/10!

four American, three Italians and three Germans are seated at random in a row. what is the probability that 1) those of the same nationality are seated together? 2)Germans are seated together and non-German are seated together

solution:

sample space 10!

1)3!4!3!3!/10!

2)2!4!3!3!/10!

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