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There are 6 pairs of black gloves and 5 pairs of white gloves. They all are put into a box and gloves are drawn one at a time. To ensure that at least one pair of black gloves is drawn out, what is the minimum number of gloves required to be drawn out?

There are 6 pairs of black gloves and 5 pairs of white gloves. They all are put into a box and gloves are drawn one at a time. To ensure that at least one pair of black gloves is drawn out, what is the minimum number of gloves required to be drawn out? Correct Answer 17

Given:

There are 6 pairs of black gloves and 5 pairs of white gloves. 

Calculation:

6 pairs of black gloves contain 6 black gloves for the left hand and 6 black gloves for the right hand.

Similarly, 5 pairs of white gloves contain 5 white gloves for the left hand and 5 white gloves for the right hand.

According to the question, we have to the minimum number of gloves required to be drawn out to ensure that at least one pair of black gloves is drawn out.

This means we have to make sure that we draw two black gloves for both left and right hands.

In order to do that, we will take the opposite approach i.e., we will try to draw the white ones first and then the black ones.

Considering,

In the first 5 attempts of drawing a glove from the box, we find 6 left white gloves.

Similarly, in the next 5 attempts of drawing a glove from the box, we find 6 right white gloves.

Nextly, we make another 6 attempts where we could only draw 6 left black gloves.

Finally, if we make a single attempt at drawing a glove, that would be a BLACK glove (right) for sure and that would complete one pair. 

Hence, minimum attempts = 5 + 5 + 6 + 1 = 17

∴ To ensure that at least one pair of black gloves is drawn out, 17 is the minimum number of gloves required to be drawn out.

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