Consider the triangular pyramids shown.

Pyramid 1
Pyramid 2
Pyramid 1 has 4 triangular sides with areas 44 meters squared, 62 meters squared, 24 meters squared, and 55 meters squared.
[Not drawn to scale]
Pyramid 2 has 4 triangular sides with areas 24 meters squared, 56 meters squared, 33 meters squared, and 14 meters squared.
[Not drawn to scale]

Pyramid 3
Pyramid 4
Pyramid 3 has 4 triangular sides with areas 26 meters squared, 60 meters squared, 31 meters squared, and 10 meters squared.
[Not drawn to scale]
Pyramid 4 has 4 triangular sides with areas 30 meters squared, 44 meters squared, 32 meters squared, and 15 meters squared.
[Not drawn to scale]

Which has the least lateral area? (Recall the formula for the area of a triangle, A = one-half b h)
Pyramid 1
Pyramid 2
Pyramid 3
Pyramid 4

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.