Dilemma for shoesDiscrete Mathematics Level 3
Little Johnny is going to attend a party and he needs to choose a pair of shoes that will suit him. In his shoe rack, he has a total of 8 pairs of distinct shoes. To help him decide, he asked his dad to choose 5 pairs of shoes at random. However, he was still unsure of what to wear, so he asked his mum to choose another 3 pairs out of the 5 chosen pairs at random. Suppose, we do not know which 5 pairs were chosen by his dad and which 3 pairs were chosen in the end, how many possible ways could there be for the 3 pairs of shoes to be chosen at random in the end?