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## Difficult Math Question #67 - Combinations

This topic has 3 member replies
800guy Master | Next Rank: 500 Posts
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#### Difficult Math Question #67 - Combinations

Wed Nov 29, 2006 2:49 pm
A shipment of 10 TV sets includes 3 that are defective. In how many ways can a hotel purchase 4 of these sets and receive at least two of the defective sets?

800guy Master | Next Rank: 500 Posts
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Fri Dec 01, 2006 5:26 pm
OA:

There are 10 TV sets; we have to choose 4 at a time. So we can do that by 10C4 ways. We have 7 good TV's and 3 defective.

Now we have to choose 4 TV sets with at least 2 defective. We can do that by

2 defective 2 good
3 defective 1 good

That stands to 3C2*7C2 + 3C3*7C1 (shows the count)

If they had asked probability for the same question then

3C2*7C2 + 3C3*7C1 / 10C4.

kulksnikhil Senior | Next Rank: 100 Posts
Joined
23 May 2006
Posted:
58 messages
2
Fri Dec 01, 2006 3:55 am
800guy wrote:
A shipment of 10 TV sets includes 3 that are defective. In how many ways can a hotel purchase 4 of these sets and receive at least two of the defective sets?
Possible ways

1> All 3 defective and 1 correct
2> 2 defective and 2 correct

1> 1 * 7 = 7
2> 3C2 * 7C2 = 6 * 21 = 126

total= 126 + 7 = 133

lalitaroral Junior | Next Rank: 30 Posts
Joined
20 Nov 2006
Posted:
10 messages
Wed Nov 29, 2006 10:22 pm
D:Defect, C:Correct

Possible combinations to select 4 TV(condition atleast 2 should be defective)

1. 3D 1C
2. 2D 2C

Case 1: 7C1*3D3
Case 2: 7C2*3D2

Total Possible ways: 7C1*3D3 + 7C2*3D2 = 84 Ways

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