Permutations & Combinations

16. In how many ways can all the letters of the word MONTREAL be arranged if the Jacob travels from home to school on his motor scooter. He can only travel on the letters R, E, A, and L must appear as the word REAL in all arrangements? roads indicated on the diagram. 0 5! School 0 4! O 51x4! O 21x5 ! Home n! 17. If (n+ 2)! = 72, then n is 12. The number of different routes Jacob can take without backtracking is 07 0 924 350 0 10 0 45 O 2520 0 7 or - 10 13. The number of distinguishable arrangements of all the letters of the word SUCCESS is 18. A 6 person health council must be created from a group of 8 doctors and 40 nurses. The expression that represents the number of different councils that 0 5 028 contain at most 2 doctors IS 0 5 040 O (40P6)+(8P1)(40P5)+(8P2)(40P4) 0 840 O (40(6)+(8C1)(405)+(8C2)(40C4) 0 420 O (40P5)(8P1)+(40P4)(8P2) 14. The expression (n -2)! (n - 1)! simplifies to O (40C5)(8C1)+(40C4)(8C2) On-2 n - 1 19. A band consisting of 4 musicians must include at least 2 guitar players. If 7 pianists and 5 guitar players are trying out for the band, then the maximum number of ways hat the band can be selected is n - 1 25 n (n - 1 ) O 210 On - 2 O 285 495 15. A 5-card hand is dealt from a standard deck of 52 playing cards. The number of different hands containing 4 diamonds and 1 spade is: O 18 590 At a local high school, each student is assigned a 6-digit identification number using O 223 080 the digits 0 to 9, where digits can be repeated. The first two digits identify the grade of the student. 0 9 295 20. How many unique identification numbers can be issued by the school to the grade O 1 115 400 12 students if the first two digits are 8 and then a 3? O 10 000 O 20 000 0 4096 0 5040