Combinatorics scenarios

[shohet.mark]

Assume we have 6 chairs and 3 men and 3 women to fill them. For the following 4 questions, I have written down how I would calculate the answer using both combinatorics and the slot method. Can an instructor please confirm the logic and approach for each? Thank you!


Q1: How many different ways can you fill the 6 seats?

combinatorics: 6! = 720
slot method: 6 x 5 x 4 x 3 x 2 x 1 = 720

Q2: How many different ways can you fill the 6 seats WITH THE RESTRICTION THAT THE MEN AND WOMEN MUST ALTERNATE SEATS?

combinatorics: 3!3!2! = 72
slot method: 6 x 3 x 2 x 2 x 1 x 1 = 72

Q3: How many different ways can you fill the 6 seats WITH THE RESTRICTION THAT THE MEN AND WOMEN MUST ALTERNATE SEATS AND THE FIRST SEAT IS FILLED BY A WOMAN?

combinatorics: 3!3!1! = 36
slot method: 3 x 3 x 2 x 2 x 1 x 1 = 36

Q4: How many different ways can you fill the 6 seats WITH THE RESTRICTION THAT THE MEN AND WOMEN MUST ALTERNATE SEATS AND THE FIRST SEAT IS FILLED BY JANE, A WOMAN?

combinatorics: 2!3!1! = 12
slot method: 1 x 3 x 2 x 2 x 1 x 1 = 12

[tim]

Looks good to me! Let us know if you have any other questions.