1. Harold (the wizard) has two kinds of elemental scrolls: sleep spells and shadow spells. Harold wishes to arrange his 7 different sleep spell scrolls and his 10different shadow spell scrolls together on the same shelf of his mystic bookcase. In how many ways can this be accomplished if all the sleep scrolls must be kept together?

a) 17!

b) (7!) (10!)

c) (8!) (10!)

d) (7!) (11!)

e) (8!) (11!)

2. A circular birthday cake is being adorned with candles, equally placed around in a circle on the top of the cake. There are eleven candles in total to be placed, each having a different colour. In how many ways can the candles be placed if the green candle must be directly beside the the orange candle?

a) 3!8!

b) 10!

c) 2!8!

d) 2!9!

e) 3!10!

3. Every week, seventy-two dancers in a large dance troupe are divided into groups and each group is assigned to create a dance in one of the styles: jazz, traditional, and hip hop. In how many ways can the dancers be divided into three groups of twenty-four dancers and all groups be assigned to perform with the jazz dance style a given week?

- The multiple choices are in the picture below.

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