2018 NJC P2 Q7

Ten circular stickers for temperature taking purposes, each of them indistinguishable apart from their colours, are placed in an opaque box.

1. It is given that four of the stickers are purple, two are blue and the remaining stickers are pink, orange, yellow and green. Suppose four stickers are given to \(4\) people, such that each person receives exactly one sticker. Find the number of ways this can be done if
   1. all four stickers are of different colours,[1]
   2. there are no restrictions on the colours of the stickers.[3]
2. The \({10}\)stickers labelled with distinct alphabets “A” to “J” are to be packed into zip-lock bags, which may come in different sizes. Bags of the same size are considered to be indistinguishable.
   1. Suppose five zip-lock bags of different sizes are used to contain \(2\) stickers each. How many ways can this be done?[1]
   2. Suppose instead that a large-sized bag is used to contain \(4\) stickers, two medium-sized bags are used to contain \(2\) stickers each and a small-sized bag is used to contain the remaining \(2\) stickers. How many ways can this be done?[2]