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Answer:
Step-by-step explanation:
We can think of the 10 pairs of gloves as simply being gloves of different colors. Picking no matching pair is the same as picking no 2 gloves of the same color. To compute the probability of doing so, we can compute the number of ways to select 8 gloves from different colors, and divide that by the total number of ways to select 8 random gloves out of the 20 gloves.
To compute the number of ways in which we can select 8 gloves from different colors, we can think of the choosing procedure as follows:
1st step- We choose from which 8 colors are we going to pick gloves from. So we have to pick 8 out of 10 colors. This can be done in ways.
2nd step - We now have to choose which glove are we going to pick from each of the chosen colors. Either the left one or the right one. For the first chosen color we have 2 choices, for the second chosen color we have 2 choices, for the third chosen color we have 2 choices, and so on. Therefore the number of ways in which we could choose gloves from the chosen colors is
And so the total number of ways in which we could choose 8 gloves from different colors is
Now, the total numer of ways in which we could choose 8 gloves out of the 20 gloves is simply
So the probability of picking no mathing pair is