Arranging seating in a theater. In how many ways can the four be seated if Elton

Question

Arranging seating in a theater. In how many ways can the four be seated if Elton John sits between William and Kate? Stacking cans. In preparation for Thanksgiving Day, the Save-You-More Store has stacked cans of pumpkin pie filling in a triangular pyramid. Shown is a 3-by-3 row of cans. The top of the pyramid is a 1-by-1 row (only one can). The second row is a 2-by-2 row (three cans), the third row is a 3-by-3 row, and so on. If the pyramid has 12 rows, how many cans are there in the pyramid? Stacking cans. Continuing Exercise 41, if the Save-You-More Store has 400 cans of cherry pie filling and wishes to build three triangular pyramids of equal height, how many rows will the pyramids have and how many cans will be left over? In Exercises 43-46, you are buying a triple-deck ice cream cone with vanilla, strawberry, and chocolate as possible flavors. The flavors can be repeated or not, and we will consider two cones to be different if the flavors are the same but occur in different order.

Explanation / Answer

Q 42

If we consider the top row as first row and then the formula for calculating the number of cans in nth row is n(n+1)/2

There are 358 cans in the pyramid

No. of Row (n) No. of Cans Required 1 1 2 3 3 6 4 10 5 15 6 21 7 28 8 36 9 45 10 55 11 66 12 72 Total 358

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