The questions are below?

1. The Board of Directors does not have assigned seats in the conference room. If there are 12 of them, seated at a round table, how many different seating arrangements are possible?

2. Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if:

a. the first letter must be Y

b. the vowels and consonants alternate, beginning with a consonant (Y is a consonant here and Y does not have to be first).

1. 12!
(12-1)! = 11! if you consider their seating arrangements relative to each other.

2. a. 1*4*3*2*1 = 24
b. 3*2*2*1*1 = 12

1. (12-1)!
2. 5!
3. 1 * 4!
4. 2! * 4!

To do possibility problems like this, you multiply the number of possibilities each time.
1. You start out with 12 people. You seat one and have 11. You seat another and have 10. Therefore, to solve this problem, you do 12*11*10*9*8*7*6*5*4*3*2*1=479001600
2. a. If the first letter it Y, you only have four possibilities to work with. 4*3*2*1=24
b. The first letter, there are 3 possibilities (three consonants). he second letter there are 2 possibilities. The third letter, you have used a consonant and are left with two possibilities. The fourth letter, there is only 1 vowel left and the fifth letter ther is only 1 consonant left. 3*2*2*1*1=12.