Answer each permutation problem. show your solution.

1. During ECQ, only 1 family member is allowed to leave the house. If there are 5 family members, and all of them are qualified to leave according to IATF, in how many ways can they schedule themselves in doing their errands?
2. In how many ways can group of 8 be arranged in a carousel?
3. Boyet has 5 shirts, 4 pants, and 3 pairs of footwear. Assuming that he may wear any of these together, how many ways can he dress himself up?
4. In a certain general assembly, three major prizes are at stake. In how many ways can the first, second, and third prizes be drawn from a box containing 20 names?
5. In how many different ways can 7 bicycles be parked if there are 5 available parking spaces?
6. Eight basketball teams are competing for the top 4 standings to move up to the semi-finals. Find the number of possible ways that they will be in first to 4th rank.
7. Find the distinguishable permutation of the word MONTALBAN.
8. Find the distinguishable permutation of the word QUARANTINE.
9. In how many ways can a group of 10 students stand in a row if three of them insist to stay together?
10. In how many ways can a group of 8 students be arranged in a carousel if 2 insist to stay together?