00:01
In this problem, it is said that a drawer contains eight different pairs of socks.
00:05
Six socks are taken at random and without replacement, and we need to find the probability that there is at least one matching pair among these six socks.
00:13
So we want to find the probability of there being at least one matching pair.
00:18
To find this, we will use the complement rule of probability, according to which this will be one minus the probability of the complementary event.
00:25
And the complementary event of there being at least one matching pair will be that there are no matching pairs.
00:32
So let's find the probability that there are no matching pairs.
00:34
So this will be the number of favorable outcomes divided by the total number of outcomes.
00:39
So what will the total number of outcomes be? so in this case, it is said that a drawer contains eight different pairs of socks, so that's eight times two, a total of 16 socks, and out of them six socks are selected at random.
00:51
This can be done in 16c6 ways.
00:54
Here we use c, which represents combination, and we use combination and not permutation in this case because the order of selection of the socks does not matter.
01:02
Next, consider the number of favorable outcomes...