Question

15to25

15.How many ways are there to seat ten people around a circular table where two seatings are considered the same when every one has the same immediate left and immediate right neighbor? 16.In how many ways can a photographer at a wedding arrange six people in a row, including the bride and groom, if a) the bride must be next to the groom? b) the bride is not next to the groom? 17.How many bit strings of length seven either begin with two Os or end with three 1s? 18.How many bit strings of length eight contain either three consecutive Os or four consecutive 1s? 19. How many permutations of the letters ABCDEFGH contain a) the string ED? b) the string CDE? c) the strings BA and FGH? d) the strings AB, DE, and GH? 20.Suppose that a department contains 10 men and 15 women. How many ways are there to form a committee with six members if it must have the same number of men and women? 21.Find the expansion of (x +y)^6 22.What is the coefficient of x8y9 in the expansion of (3x+2y)^17 23.What is the solution of the recurrence relation an a,n-1+2an-2 with ag 2 and a, =7? 24.What is the solution of the recurrence relation a,n =6 an-1 -9an -2 with ag 1and a, 6? 25.What is the solution of the recurrence relation an -6 an-1-11a,-2 +6a-3 with ao =2 and aj =5 and a2=15?

Answer 1

expansion of y binomial theoern tuse SA +-- - (2) eshere k! (n-k)! m 12 o! (x 3,6-3 + 4.6-4 6-1 2. 6-2 S5-S 42 61 o! (6-0)! 116-1)! 2 6-2)! 31 -3)! 4/4) 01 5!65)1 CIC) 6. 5! 3 y.4.3 .2)31 $3 1

DATE 20 PAGE No 1 is expansion 22 exbansion of (at2y) 25 29 ! 8 (1+-8)! 17! AM 8) 9 Huther expansion 17. 161S4. 13.12.11. 10.9 13.11, lo 3 12.11 la 4561)12) 8166 29299 2 23. diven Aecursence ela tion an- an--2am-9- (2) Equetlion characteriatic above selation in a d -2 NO -2d-2- (at)-2(+1)- 2-

PAGE No uar A (2) +A (-1)n (2) irg iven rilial canali Hend in ) n-o A, (2 A. L (4) ut in (3) 4 A,(2)' 2A-A adding 8A 9 A 9/ 3 Az= 9- Ar = 2-3 - Aave A 3 onol Ag-1 in 13) the se valia put get we is sal of gisern Lelotin decunence 24 glen seausienca selation 6ant-9an-2 uaith a adl a ()

PAGE No the aiboe ea -6 a 9 ZO Cac- 3)2 iA given hy LALTNA) (3 (2) sing initial Coualttion coe hasce n-o CAto) (3) fer a4-6 C4 (ATt 1A, 26-(1 A,) 2 ud nl im (2) esig(3) 1P A 2 A1 Ai (2) t thele valuos in LLt n1) (3) soln decumence elation

PAGE No 25 aiven secstenco selation s an-6an--11a- &than- bant1am haa characteststic en aabeive delation fn a ls 6&2 11 - 6 0 A 1 lesty T-6 t11-6 c 12- 12 -0 -) is factor ol 2)divide(2) -S2tl- - Sa+Sa- 3-602+1l0- ut this valhee in (2)urged (dCa2-Colt) Ce-e tel-3)-2la-o al-2) (e-2) =し2」3 the sal"of

PAGE No A (2)t A la) A (3 mi-tial condlitionsne have (3) A, (2 A At t AzpA3 in 3) A (5) APaAp t 3A in (3) PA2 A (3)2 (6) IS A t 4A 9A, aubtract 4) troms nd 4) Pm6 A t2 A SA, +8 A 17 with Q) and sabtaet Paem(8) (8) 13 and ultihy 7 4ニ2A2 3- 9(9) 3-4=-) A2 = 3- 2A2- A -A,- A 2 - (-)-22 1 e hare Ais, Ar-L A 2 mputh in (3) gel 1+2212) (2+23 ia pal ef gisen sebtion