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Quandaries & Queries
Q & Q
 Topic: multiplication principle
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Choices at a restaurant 2009-04-13
From Rob:
There is a restaurant you get:

Rice/Noodles (1) Main Ingredient (any) Sauce (1)
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7
8
9
10
11
12

So the question is how many different combinations are there. You can only have 1 rice/noodles in a selection and only 1 sauce in a selection but you can have between 1 and all twelve mains in a selection. there are 7 rice/noodles , 12 mains and 6 sauces. How many possibilies. I did it mentally in the restuarant, no pen, paper or calculater and i got 3276..i think thats wrong. please help

Rob
Answered by Robert Dawson, Stephen La Rocque and Claude Tardif.

Danging couples 2001-06-06
From Danielle:
How many boy-girl dancing couples could be formed if 85 boys and 102 girls attend a school dance?
From Linda:
Your DJ Business has 6 rap, 10 rock, 6 alternative, 8 oldies, and 5 country CD singles. How many different 10-song sets can the DJ play, if she plays 2 singles from each category? and How many different 10-song sets if she plays exactly 3 rap singles and 4 rock singles in each set?
Permutations and Multiplication Principle 2000-09-22
From Candice:
A forester selects 4 pink and 4 white dogwoods. The trees are to be planted in row. If a tree is distinguished by color only, in how many ways can the eight dogwoods be planted? How many of these arrangements have at least two trees of the same color side by side?
Answered by Denis Hanson and Claude Tardif.
towers of cubes 1999-10-05
From Sanker:
I need help to solve this Rules for bulding towers of cubes
 rule 1 The number of cubes on the bottom layer is always one less than the number of squares on the grid rule 2 Each new layer is made with one cube less than the layer underneath it.
1. Investigate how many different arrangements there are of 4 cubes on top of 5 cubes on a two by three grid

2. investigate the number of different arrangements of six cubes on top of seven cubes on a two by four grid

3. investigate the relation between the number of arrangements of cubes and the size of the grid
• when there are two layers of cubes
• when there are more than two layers of cubes