Question Bank  Probability

OA : 7/16

4C2 * D(2)/4! = 1/4

10 sets (10_11_12.....19)
Each set 9. So 9c2.
10 * 9c2/90c2 = 8/89

HCF=1 and their LCM is their product so zero

OA : 1/2

(10,6,6) : 3 * 1/9 * (1/3)^2 = 3/81 = 27/729
(10,10,6): 3 * (1/9)^2 * (1/3) = 3/243 = 9/729
(10,10,2): 3 * (1/9)^2 * 5/9 = 15/729.
(10,10,10): (1/9)^3 = 1//729
dd: (27+9+15+1)/729 = 52/729

Consider 3 consecutive HHH case. :
HHHHH,HHHHT,HHHTH,HHHTT,THHHT,TTHHH,HTHHH,THHHH so total 8 cases. similarly for TTT we get 8 cases. Total cases = 16
P = 16/32= 1/2

all three are of form 3k=5c3
all three are of form 3k+1 = 5c3
all three are of form 3k+2 = 5c3
one is 3k,one is 3k+1 and one is 3k+2 = 5c1 * 5c1 * 5c1=125
so total 125+30=155
total cases = 15c3 = 455
probability = 155/455= 31/91

a + b + c = 12. so 11C2
6 + a + b + c = 12. so 5C2.
so 11C2  3 * 5C2 = 553 * 10 = 25.
so 25/216

OA : required probability is 1