Four unbiased six-sided dice are thrown simultaneously. What is the number of ways to obtain a total sum of 23 on all the dice?

A box contains 20 black, 22 white, and 24 red socks. If a person draws socks at random one by one without looking, what is the minimum number of socks she must pick to be certain of having at least one pair of black socks?

Die A consists of numbers 1, 3, and 5 on three faces, and 0 is marked on the remaining three faces. On the second die B, the odd numbers 1, 3, and 5 are replaced by twice their values (2, 6, and 10), and the remaining three faces consist of 2, 4, and 6. Both dice are thrown together and the product of the numbers obtained is taken. If we list all possible outcomes, which product will be obtained exactly three times?