How many ways can we divy this up?

You figure it out, I'm eating.

Whose counting the E-Numbers boys by flickr user law_keven

In how many ways can 8 books be arranged on a shelf, if 3 particular books must be together?

There are 10 football teams in a certain conference. How many games must be played if each team is to play every other team just once?

There are 10 football teams in a certain conference. How many games must be played if each team is to play every other team just once?

There are 9 chairs in a row. In how many ways can 4 students be seated in consecutive chairs? (Hint: First find the number of ways of choosing 4 consecutive chairs.)

Seven people reach a fork in a road. In how many ways can they continue their walk so that 4 go one way and 3 the other?

Poker CombinationsGiven a standard deck of 52 cards, how many ways are there to draw 5 cards to obtain each hand.

(a) Royal Flush [ace, king, queen, jack, ten in the same suit]

(b) Straight flush [five cards in sequence and of the same suit, but not ace king queen jack ten]

(c) Four of a kind [four cards of one face value and one other card]

(d) Full house [3 cards of one face value and 2 cards of another face value]

(e) Flush [5 cards of the same suit but not in sequence, not including the straight flush and royal flush above]

THE REST OF THESE QUESTIONS ARE HOMEWORK

(f) Straight [5 cards in sequence, but not all of same suit. Ace high or low]

(g) Three of a Kind [exactly 3 cards of one face value and 2 different cards]

(h) Two pairs [one pair of each two different face values and a card of a third face value]

(i) One pair [two of one face value, and 3 cards of different face values, no matching the pair]

(j) No pairs [5 different face values, not in sequence, not all cards in the same suit]