Couple PS problems Need help!!

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Couple PS problems Need help!!

by kguo » Sun Oct 11, 2009 6:02 pm
1. ((1001)^2 - (999)^2) / ((101)^2 - (99)^2)

1)10
2)20
3)40
4)80
5)100



2. From a group of 21 astronauts that includes 12 people with previous experience in space flight, a 3 person crew is assembled in which exactly 1 person in the crew has experience in space flight. How many different crews of this type is possible.

1)432
2)594
3)864
4)1330
5)7980

both answers are a[/spoiler]
Source: — Problem Solving |

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by sanjana » Sun Oct 11, 2009 10:36 pm
1)
1001 = 1000+1
999 = 1000-1

101 = 100+1
99 = 100-1

Therefore the given expression becomes,

((1000+1)^2 - (1000-1)^2)/((100+1)^2 - (100-1)^2))

Now apply a^2-b^2 = (a+b)(a-b) to both the NR and DR.

it will reduce to

(2000*2)/(200*2) = 10 (a)

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by sanjana » Sun Oct 11, 2009 11:51 pm
2)
Total : 21 Astronauts
Experienced : 12
No experience : 21-12 = 9

No of combinations with 1 exp and 2 Non experienced :
9c2 * 12 c1 = 432