Binita is giving away thirty identical wine glasses as favours at her latest party! Six guests in total are attending the party. In how many ways can the favours be given out if Binita wants to ensure that each guest gets at least five wine glasses? A ( 30 ) ( 30 ) ( 30 ) ( 30 ) ( 30 ) O B. 1 30 OC 55 5 555 O D. O 30 OE. 6 6666The airport sells thirty-one different kinds of cookies. Thirteen of these kinds can be purchased only as small cookies and the other eighteen kinds can be purchased only as large cookies. The small cookies cost $2 each and the large cookies cost $5 each. While waiting for her flight, Angelika decides to order exactly $20 worth of cookies, with each cookie she orders being a different kind. How many different orders can she make? 31 31 31 O A. 10 0 21 5 2 24 + (0 4 27 O B. (10 ) ( 8 ) + 6 ( ) +6 6 O c. ( 18 ) (18 ) +(13 ) ( 2 ) + (18 ) ( 18 ) O D. 3 E. 1310180 + 135182 + 13 184Joey has fourteen photos of his friends. In how many ways can he choose eight of the photos to add to his photo album? 14! OA . 6! 14! O B. 8 ! O C. 6! OD. 14 8 O E. 214A 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 orange candle must be between the white candle and the magenta candle? O A. 3!10! O B. 3!8! O c. 10! O D. 219! O E. 2!8!Jay is an overworked clerk in a store that is open 6 days a week, 12 hours a day, with clerks working 6-hour shifts. Jay gets exactly 3 days off (that is, 3 days where the store is open, but Jay isn't working) each week, but they are not necessarily 3 days in a row. On workdays, Jay always works the earlier shift, but sometimes has to work a double shift (work the whole 12 hours). Next week, Jay has to work 2 double shifts. How many different schedules could Jay have next week? O A . 7 O B. 32 2 O c. ( 3 2 21 6 O D. 321 O E. (7)The PTA is forming a subcommittee to purchase new equipment for the school's lacrosse team. There are nine parents and thirteen teachers who are available to join this 6-person subcommittee. In how many ways can the subcommittee be formed if there must be at least 1 parent on it? 22 13 O A. 6 6 9 OB. 6 22 9 O c. 6 13 OD. 2 ) -(2 ) 6 13 OE. 6Every week, forty-four dancers in a large dance troupe are divided into groups and each group is assigned to create a dance in one of the styles: electric boogaloo, jazz, Irish folk, and fusion. In how many ways can the dancers be divided into four groups of eleven dancers and each group assigned to a different dance style in a given week? 44 O A. : 3 ! 11 11 11 11, 44 O B. 11 11 11 11, 44 O C. 4 X 11 11 11 11, 44 O D. 4! X 11 11 11 11/ 44 O E. : 4! 11 11 11 11Harold (the wizard) has two kinds of elemental scrolls: fire spells and teleportation spells. Harold wishes to arrange his 7 different fire spell scrolls and his 9 different teleportation spell scrolls together on the same shelf of his mystic bookcase. In how many ways can this be accomplished if the scrolls must alternate elemental type? OAO O B. 2(7!) (9!) O C. 7! + 9! O D. (7!) (9!) O E. 1