6th Grade Math Textbook, Fundamentals

Lesson 12-8 for exercise sets. &KDSWHU 

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1.In how many ways can you choose 4 types of fish from an aquarium of

10 different fish?

2.Five people in a room decide to shake each other’s hands once.

How many handshakes will there be altogether?

3.The school orchestra has 10 flute players and 6 violinists. In how many

different ways can 2 flute players be selected to play at a concert?

4.Discuss and Write Give an example of a combination and a permutation.

Key Concept

Combinations

When you have a list of nitems and you want to know the number of combinations

with only ritems, where r n:

• Find the number of permutations of picking robjects from a group of nobjects.


• Then divide by the number of permutations of robjects.

When the numbers involved in finding the number of combinations
(and permutations) become very great, you can use a calculator.

Your Uncle Joe is taking family photographs at a picnic. He randomly
selects 6 people at a time from the 51 gathered and takes their picture.
How many different groups of 6 people could he select to photograph?

Here are the steps to find the number of different combinations
by using a graphing calculator.

First enter the total number of objects, 51.

Then press.

Use the right arrow key

to highlight PRB.

Press 3. This will select nCr.

Then press the number of objects being

considered. In this case, enter 6 for the

six people chosen at random.

Press.

So there are 18,009,460 different combinations possible.

To find a permutation,

press 2 to select nPr.

To find a factorial,

press 4 to select !,

the factorial symbol.