12bhang wrote:
Hi Karishma,
Could you please tell me how I'm going wrong?
Since there are 3 blue pairs and 2 green pairs, we have a total of 10 gloves.
I considered two cases:
Case 1: we have a blue pair match
This can be done if we have a blue left, a blue right and any other glove. So,
Since we have 3 blue lefts and 3 blue rights and a total of 10 gloves,
3C1*3C1*8C1- 3 ways of selecting a blue left, 3 for a blue right and any one glove of the remaining 8=72 ways.
You are double counting here. Say the gloves are all distinct. The 3 blue left ones are Bl1, Bl2 and Bl3. Three blue right ones are Br1, Br2, Br3.
So you select one of the blue left ones and one of the blue right ones: Bl2, Br3.
Now you have 8 leftover and you can select any one of them. Say you select Bl1.
So your selection consists of Bl1, Bl2, Br3
Imagine another scenario:
So you select one of the blue left ones and one of the blue right ones: Bl1, Br3.
Now you have 8 leftover and you can select any one of them. Say you select Bl2.
So your selection consists of Bl1, Bl2, Br3
The two selections are the same but you have counted them as different selections.
12bhang wrote:
Case 2: we have a green pair match,
SO, Gleft,Gright and any other glove,
2C1*2C1*8C1=32
Summing , we get 104
The total number of ways to select 3 gloves =10C3=120
so probability of getting a match=104/120 = 13/15.
Where am i going wrong?
Same problem with the green pair.
From the solutions given above, review how to effectively use probability to solve this question.
In case you want to use combinations, you still have to take cases:
All three Blues:
3C2*3C1*2 = 18(Select 2 of the blue left and one of the blue right. Multiply by 2 because you can select 2 of the blue right and one of blue left too)
2 Blues, 1 Green:
3C1*3C1*4C1 = 36
2 Greens, 1 Blue
2C1*2C1*6C1 = 24
Three Greens
2C2*2C1*2 = 4
Total = 82
Select 3 gloves from 10 in 10C3 ways = 120
Probability = 82/120 = 41/60