Factorial and combinations question.

Question

Any help with these would be greatly appreciated...

1) How many arrangements are there of the letters of the word SAUSAGES ? if the A’s must be together and the S’s apart? (answer apparently 240 ways)

2) A team of 5 people is to be chosen from 7 Girls and 6 Boys, how many teams are possible if there must be more girls than boys and Julie (a girl) can’t be on the same team as Michael (a boy). (answer apparently 661)

Thanks a lot. I really need urgent help with this.

Answer 1

Hints: 1) use the inclusion-exclusion principle,

2) If there are more girls than boys on the committee of five, you have three choices: $(0,5), (1,4), (2,3)$. Then you choose $j$ from the set of boys and $5-j$ from the set of girls.