1.How many ways can the letters in the word LOVE be arranged?

2 How many ways can 3 men and 2 women sit in a row if the men and women must alternate?

3. Anna is choosing and arranging a set of 3 dresses from a set of 10 dresses. How many ways are possible?

4. In a school club, there are 5 possible choices for the president, a secretary, a treasurer, and an auditor. Assuming that each of them is qualified for any of these positions, in how many ways can the 4 officers be elected?

5. There are twelve contenders for the singing contest. The judges committee will choose three of them, and rank them 1st, 2nd and 3rd placer. How many ways are possible?

6. suppose that in a certain association, there are 12 elected members of the Board of Directors. In how many ways can a president, a vice president, a secretary, and a treasurer be selected from the board?

7. How many ways can you place 9 different books on a shelf if there is space enough for only 5 books?

8. A high school plays 15 Futsal games during season. In how many ways can the team end the season with 8 wins, 4 lossers, and 3 ties?

9. How many distinguishable permutations are possible with all the letters of the word BAYANI HAN?

10. Five couples want to have their pictures taken. In how many ways can they arrange themselves in a row if
a couples must stay together?
b. they may stand anywhere?

(SHOW YOUR SOLUTION)​