My daughter age 11 can't do this, and I can't help her. Could someone explain very basically how to solve it please.

Many thanks

PROBLEM

Draw an X and Y plan, with the coordinates of O being your origin (0,0). Plot A with coordinates (2,0), B (3,0) and C (2,1).

Now in this question journeys are made of steps of whole-numbers length in any combination of directions left, right, up or down. Also one may retrace steps. So, for example, it is possible to travel from O to the point (2,1) by journey OAC which has length 3, it is possible to get to (2,1) by a different journey, OBAC which has length 5.

a) Starting from O, how many possible destinations (including O) are there with journeys of length

1) 2?

2) 3?

b) How many different journeys of length 3 are there starting at O and finishing at (1,0)?

c) You are given that the sum 1+2+3+....+100 = 5050

How many journeys of length 102 are there from O to coordinate (100,0)?