Question:

How many ways may 4 males and 4 females be seated around a circular table if we must have alternating gender (male, female, male, female etc) and two individuals (lets call them Betty and Jim) must not be seated next to each other?

Note: As an additional part to this question you are required to produce a diagram explaining your working or a detailed description as to why your answer is the only answer. Students often have difficulty with these questions, often neglecting to adjust for symmetry or rotations. If you are unsure of your answer try a smaller subset and work up i. e. 2F and 2M then 3F and 3M and see if you can see a pattern in the working (this is how I get students to start to think about the complexity of these problems, with smaller sub problems).

What is the solution set of the quadratic inequality x^2-5< or equal to 0

The table below lists recommended amounts of food to order for 10 party guests. how much of each food item should nathan and amanda order for a graduation party with 55 guests? use the table to answer. item amount fried chicken 16 pieces lasagna 7 pounds deli meats 1.8 pounds sliced cheese 1 and two fifths pounds bakery buns 1 dozen potato salad 2 pounds

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.