# Practice Problems Project 5

Here are some practice problems to help you work through Pascal’s Identity:

From the Chapter 5 (see pages 241-242) project try:

• 1
• 2 We did this at the end of class–this is essentially your extra credit assignment
• 3 This is what we spent most of the class period talking through. Try to write down an explanation, and then check your work with your lectures notes.
• 4
• Challenge problem: 5 part a

The following problems are not in your text book:

• Use Pascal’s Identity to generate C(n,r) for all n and r less than or equal to 8.
• Assuming that C(6,2)=C(6,4), use Pascal’s Identity to show that C(7,2) is equal to C(7,5). Do not use the formula $\binom{n}{r}$. (Hint: Convince yourself that C(6,1)=C(6,5)=6.)
• A student group is forming a committee with 3 members. Assuming there are 56 possible ways to choose the members of the committee, how many members does the student group have? (Hint: Use your work from the first of these problems.)

Selected Solutions: