Problem

Explain the connections between Exercises 1, 2, and 3.Exercise 1Show that n+1Cr = nCr-1 +...

Explain the connections between Exercises 1, 2, and 3.

Exercise 1

Show that n+1Cr = nCr-1 + nCr.

Exercise 2

The array commonly called Pascal’s triangle can be defined by giving enough information to establish its pattern.

(a) Write the next three rows of Pascal’s triangle.


(b) Give a rule for building the next row from the previous row(s).

Exercise 3

Pascal’s triangle can also be defined by an explicit pattern. Use the results of Exercises 4 and 5 to give an explicit rule for building the nth row of Pascal’s triangle.

Exercise 4

(a) Find the number of subsets of each possible size for a set containing four elements.


(b) Find the number of subsets of each possible size for a set containing nelements.

Exercise 5

The array commonly called Pascal’s triangle can be defined by giving enough information to establish its pattern.

(a) Write the next three rows of Pascal’s triangle.


(b) Give a rule for building the next row from the previous row(s).

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Solutions For Problems in Chapter 3.2