1.  Assigning seats

Five girls and three boys are to be assigned to eight seats in a row, with the stipulation that a girl sits in the second seat. How many arrangements are possible? 

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2. Assigning seats, again

Four girls, two boys, and five cats are to be assigned to 11 seats in a row, with the stipulations that a girl sits in the fourth seat, a boy sits in the sixth seat, and a cat sits in the seventh seat. How many arrangements are possible? 

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3. Cube and octahedron

A standard cubical (6-sided) die and an octahedral (8-sided) die are each rolled n times. What is the smallest value of n for which the total number of possible outcomes for the octahedral die is at least twice the number for the cubical die?

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4. Subtracting the repeats, 3 chosen from 4

Repeat the task of Problem 1.3(a), but now in the case where you pick triplets from four people (instead of five).

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5. Subtracting the repeats, 4 chosen from 4

Repeat the task of Problem 1.4, but now in the case where you pick quadruplets from four people (instead of five).

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6. Subtracting the repeats, 4 chosen from N

Repeat the task of Problem 1.4 (or Exercise 5), but now in the general case where you pick quadruplets from N people, instead of five (or four).

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