michael has 10 pairs of black socks,8 pairs of white socks&7 pairs of green socks everything is mixed in a drawer. as there is no light he is not able to identify the colour of the socks . how many of the socks will he have to take to match 1 pair

Minimum 2, maximum 4.

To determine how many socks Michael will have to take to match a pair, we need to consider the worst-case scenario where he selects socks of different colors with each pick.

Let's break it down:

First, he needs to match one pair of socks. Since each pair is made up of two socks, he needs to take a minimum of two socks.

In the worst-case scenario, for each subsequent sock, Michael will keep selecting a sock of a different color from the previous ones. This way, he ensures that he doesn't accidentally match a pair until he gets a matching pair.

So, for matching the first pair, he takes two socks.
For each additional sock he takes, the probability that it matches one of the previous socks decreases. To maximize the number of socks he has to take, he should always select a sock of a different color from the previous ones.

Given that Michael has:
- 10 pairs of black socks (20 black socks in total),
- 8 pairs of white socks (16 white socks in total), and
- 7 pairs of green socks (14 green socks in total).

The maximum number of socks he needs to take before matching a pair can be calculated as follows:

For the first sock, he can pick any sock, so there are 20 + 16 + 14 = 50 socks to choose from.
For the second sock, he needs to avoid selecting a sock of the same color, so there are 50 - 2 = 48 socks remaining for selection.
Similarly, for the third sock, he needs to avoid selecting a sock of either of the previous two colors, giving him 50 - 4 = 46 socks remaining.

We can see a pattern emerging:
- On the first pick, he has 50 socks to choose from (any color).
- For each subsequent pick, he reduces the number of socks available by 2 (to avoid matching a pair).

Using this pattern, we can calculate the total number of socks Michael will have to take to match a pair:

2 (for the first pair) + 2 (for the second pair) + 2 (for the third pair) + ... until the final pair.

Now, we need to find the last pair of socks that he can match. Since he has 10 pairs of black socks, 8 pairs of white socks, and 7 pairs of green socks, the maximum number of pairs he can match is 7.

Therefore, the total number of socks Michael will have to take to match a pair is:

2 + 2 + 2 + ... + 2 (7 times)

This can be calculated as: 2 * 7 = 14.

Hence, Michael will have to take a minimum of 14 socks to match one pair.