A circular birthday cake is being adorned with candles, equally placed around in a circle on the top of the cake. There are twelve candles in total to be placed, each having a different colour. In how many ways can the candles be placed if the blue candle must be between the beige candle and the black candle? O A. 3!11! O B. 3 l9! 0 C. 11! O D. 2!9! O E. 2! 10! Reset Selection Every week, forty-five dancers in a large dance troupe are divided into groups and each group is assigned to create a dance in one of the styles: traditional, Irish folk, and ballet. In how many ways can the dancers be divided into three groups of fifteen dancers and each group be assigned the same dance style in a given week? O A . 45 15 15 15) : 2! O B. 3! X 45 15 15 15 45 Oc. 15 15 15 : 3! 45 O D. 3 X 15 15 15 O E. 45 15 15 15 Reset Selection18! Devon has 10 different science fiction novels and 8 different romance novels. If he wishes to select 5 novels to read on his upcoming business trip, in how many ways can this be done? O A. 5! O B 10 + u oo O c . 18 5 O D. 218 O E . ('S ) X Reset SelectionThe PTA is forming a subcommittee to purchase new equipment for the school's swim team' There are twelve parents and thirteen teachers who are available to join this 6-person subcommittee. |n how many ways can the subcommittee be formed if there must be at least 1 teacher on it? \"('62) OR (?)-(')-(?) 0 C ('3) 0 D, (2:) - (if) \"Ga-('3) Reset Selection Megumi is giving away nine identical wine glasses as favours at her latest party! Five guests in total are attending the party, In how many ways can the favours be given out if Megumi wants to ensure that each guest gets at least two wine glasses? OA.0 03.29 OC-(Z)()()(3)(i> O D~ (2) (2) 05.1 Reset Selection Siblings Beth and Ibrahim both have their birthdays this month. Their parents have bought a total of twenty different toys for the two. Since Beth is turning four years old and Ibrahim will be fourteen years old, their parents will give Beth four of the toys, while Ibrahim will be gifted fourteen. The remaining toys will be donated to the local orphanage. In how many ways can the toys be given out? O A . ( 24 ) ( 24 ) ( 20 ) O B. 20 (4 14 2 O c. (20 ) (24 ) O D. 4!14!2! O E. 3! 20 4 14 2 Reset SelectionThe airport sells twenty-nine different kinds of cupcakes. Eighteen of these kinds can be purchased only as small cupcakes and the other eleven kinds can be purchased only as large cupcakes. The small cupcakes cost $4 each and the large cupcakes cost $5 each. While waiting for her ight, Claudia decides to order exactly $48 worth of cupcakes, with each cupcake she orders being a different kind. How many different orders can she make? 0 A~ + (7 i918) + (2 $919) 0 3' (13(3) + (178 )(141) + (128x181 ) 12 o 7 4 2 8 0'(4)(1)+(2)(2) 0 5.1812110 +187114 +182118 Reset Selection