5 quick math problems

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9.
+ -/1 points HunterDM3 4.3.030.
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Suppose that 100 lottery tickets are given out in sequence to the first 100 guests to arrive at a party. Of these 100 tickets, only 15 are winning tickets. The generalized
pigeonhole principle guarantees that there must be a streak of at least / losing tickets in a row. Find I.
1 =
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8.
+ -/1 points HunterDM3 4.3.028.
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A small college offers 234 different classes. No two classes can meet at the same time in the same room, of course. There are 11 different time slots at which classes can
occur. What is the minimum number of classrooms needed to accommodate all the classes?
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7.
+ -/1 points HunterDM3 4.3.018.
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Suppose you have ten squares of stained glass, all of different colors, and you would like to make a rectangular stained glass window in the shape of a 2 x 5 grid.
WebAssign Plot
How many different ways can you do this, taking symmetry into account? (Note that any pattern may be rotated 180°, flipped vertically, or flipped horizontally. You should
count all the possible resulting patterns as the same window.)
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2.
+ 0/1 points | Previous Answers HunterDM3 4.3.006d.
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The following figure consists of 8 horizontal lines and 15 vertical lines. The goal of this problem is to count the number of rectangles (squares are a kind of rectangle, but
line segments are not).
Let V be the set of all sets of two vertical lines, and let H be the set of all sets of two horizontal lines. Let R be the set of all rectangles in the figure. Define a function
f:
RVXH by
A
с
({AB, CD}, {AC, BD}).
B
D
Compute R1, the number of rectangles in the figure.
1638
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1.
+ -/1 points HunterDM3 4.3.004b.
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The following 9 x 26 grid is divided into squares that are 1 unit by 1 unit.
B
А
The shortest possible path on this grid from A to B is 35 units long. One such path is shown in the figure. Let X be the set of all 35-unit-long paths from A to B.
Compute XI, the number of 35-unit-long paths from A to B.
1X1 =
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