McGraw Hill Glencoe Algebra 2, 2012
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McGraw Hill Glencoe Algebra 2, 2012 View details
4. Counting Techniques
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Exercise 18 Page P12

Is the order important?

Permutations or combinations? Combinations
Answer: 220

Practice makes perfect

We want to find how many ways there are to select 9 out of 12 books from the list. Note that, in this case, the order is not important. Therefore, the situation involves combinations. To calculate the answer, we will use the formula for combinations of n objects taken r at a time. _n C_r = _n P_r/r! ⇔ _n C_r = n!/(n-r)!r! In our exercise, n= 12 and r= 9. Let's substitute these values into the above formula.

_n C_r = n!/(n-r)! r!
_(12) C_9 = 12!/( 12- 9)! 9!
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Simplify
_(12) C_9 = 12!/3! 9!

Write as a product

_(12) C_9 = 12* 11* 10* 9!/3! 9!
_(12) C_9 = 12* 11* 10/3!

Write as a product

_(12) C_9 = 12* 11* 10/3* 2* 1
_(12) C_9 = 1320/6
_(12) C_9 = 220

There are 220 ways to select 9 of 12 books.