Chapter 3.2 questions 2 and 3 page 113

2. In how many ways can we choose five people from a group of ten to form a commitee?

\[p=\frac{a!}{b!(a-b)!}\]

\[p=\frac{10!}{5!(10-5)!}\]

\[p=\frac{3628800}{120 *5!}\] \[p=\frac{3628800}{120 *5!}\] \[p=\frac{3628800}{14400}\] \[p=252\]

Now lets test this in R using the choose function:

choose(10,5)
## [1] 252

3. How many seven-element subsets are there in a set of nine elements?

\[p=\frac{a!}{b!(a-b)!}\]

\[p=\frac{9!}{7!(9-7)!}\]

\[p=\frac{362880}{5040 *2!}\]

\[p=\frac{362880}{10080}\]

\[p=36\]

Now lets test it with R.

choose(9,7)
## [1] 36