FUNDAMENTAL PRINCIPLE OF COUNTING

How many ways can 6 students be seated in a row?

In how many ways can 10 true-or-false questions be answered? Assumed you leave none of the questions blank?

James has three-letter password that uses only vowels for his computer. How many different passwords are possible?

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Keypieyssssviz Keypieyssssviz · Answer 1

FUNDAMENTAL COUNTING PRINCIPLES

— it states that if there are n ways of doing something, and m ways of doing another thing, then there are n x m different ways to do both.

1) n = 6!

6! = 6•5•4•3•2•1

= 720

therefore, there are 720 ways

2) n = 10!

10! = 10•9•8•7•6•5•4•3•2•1

= 3,628,800

therefore, there are 3,628,800 ways

3) n = 3!

3! = 3•2•1

= 6

therefore, there are 6 different possible ways

hope it helps

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