10) formula to find the answer is n-1C2

here n = 12
so 12-1C2 = 11C2= 11 *10 /2 = 55


4) let us assume that they travelled x kms on the first day of the trip.
so on the second day they travelled x +20 kms and x+2*20 kms, x+3*20 kms in third and fourth day respectively.

So the total distance they travelled is
x+ (x+20) + (x+2*20). . .+(x+8*20) = 1080
9x + (1+2+3+...+8)*20 = 1080
9x + (8*9/2) *20 = 1080
9x + 720 = 1080
9x = 1080 -720 = 360
x = 360/9 = 40

a. kms did they travel on the 4th day = 40 + 3*20 = 100 kms
b. kms did they travel on the last day = 40 + 8*20 = 200 kms

5) Porbablility = n(A)/n(S)

n(S) = 1000 x 1000

n(A)
----

if A says 1 then B can say any number between 2 to 1000=> 999 diff ways
if A says 2 then B can say any number between 3 to 1000=> 998 diff ways
if A says 3 then B can say any number between 4 to 1000=> 997 diff ways
. . .
if A says 999 then B can say only 1000=> 1 possible way
if A says 1000 then B can't say any number=> 0 possible ways

so n(A) = 999 + 998 + . . . +1 = 1000 x 999 /2

So probability that B tells a number which is greater than the number told by A= 1000 x 999 / 2 x 1000 x 1000 = 999/2000