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1. How many ways can 7 books be arranged in a shelf if 3 particular books must beseparated?

2. In how many ways can we put 4 people in 10 rooms if twoof them must stay in the same room, other in separate room.

3. 4boys and 5 girls are to be seated in a row. In how many ways can this be doneif thegirls and boys must be seated alternatively.

4. 4 booksand 6 magazines are to be arranged in 2 rows of 5 copies each. At least 2 booksmust be on the first row and at least 2 magazines must be on the second row.What is the total number of arrangements?

5. A and B invite 8 friends to a party. The participants are arranged in 2 rows of 5 in order to take photos. Find the number of arrangements if

(a) No restriction.

(b) A and B are next to each other.

thank you