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 15 Page P12

Is the order important?

Permutations or combinations? Combinations
Answer: 15

Practice makes perfect

We want to find how many ways there are to select 2 out of 6 pizza toppings. 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= 6 and r= 2. Let's substitute these values into the above formula.

_n C_r = n!/(n-r)! r!
_6 C_3 = 6!/( 6- 2)! 2!
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Simplify
_6 C_2 = 6!/4! 2!

Write as a product

_6 C_2 = 6* 5* 4!/4! 2!
_6 C_2 = 6* 5/2!

Write as a product

_6 C_2 = 6* 5/2* 1
_6 C_2 = 30/2
_6 C_2 = 15

There are 15 ways to select 2 out of 6 pizza toppings.