SOLUTION: 1) In how many ways can 5 seats on a bench be assigned from amongst 12 people? 2)John and Harry Invited four other people to sit on their bench. In how many ways can these six p

Question 198486: 1) In how many ways can 5 seats on a bench be assigned from amongst 12 people?
2)John and Harry Invited four other people to sit on their bench. In how many ways can these six people be seated on this bench if:
a)there are no restrictions
b)john is seated at the left end and Harry is seated at the right end
c)John and Harry must be seated together.
3)You bought five house numbers at your lumber supply store. The numbers are 1,2,3,4 and 5.How many three-digit house numbers a)are even? b)are possible?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1) In how many ways can 5 seats on a bench be assigned from amongst 12 people?
If you count arrangements,
there are 12C5 = 792 ways
Each of these sets of people can be arranges in 5! = 30 ways
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Total # of arrangements = 792*30 = 23760 way
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2)John and Harry Invited four other people to sit on their bench. In how many ways can these six people be seated on this bench if:
a)there are no restrictions: 6! = 720 ways
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b)john is seated at the left end and Harry is seated at the right end
4! = 24 ways
--------------------------
c)John and Harry must be seated together.
5! = 120
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3)You bought five house numbers at your lumber supply store. The numbers are 1,2,3,4 and 5.
How many three-digit house numbers
a)are even?
pick the units digit: 2 ways
pick the 2nd digit: 4 ways
pick the 1st digit: 3 ways
Total # of ways: 2*3*4 = 24
---
b)are possible? 5*4*3 = 60 ways
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Cheers,
Stan H.

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