2021 EJC P2 Q8
Mei Li has $3$ types of gemstones comprising $6$ Emeralds, $4$ Sapphires and $3$ Labradorites. All the gemstones are of different sizes.
(i)
Find the number of ways Mei Li can arrange all the gemstones in a circle, where the biggest of each type of gemstone are together.
[2]
(ii)
Next, Mei Li selects $9$ gemstones with $3$ of each type to arrange in a circle. Find the number of ways to do this, such that the gemstones alternate in the following order, clockwise: Emerald, Sapphire, Labradorite.
[3]
(iii)
Finally, Mei Li decides to randomly arrange all $13$ gemstones in a row. Find the number of ways to do this, such that no two Sapphires are next to each other and the Labradorites are all together.
[3]
Mei Li selects $7$ gemstones to be showcased at a conference.
(iv)
Find the number of ways to select the gemstones such that at least one of each type is selected.
[3]
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