Question 3
A flea at point $A$ on a line jumps exactly $1\,\mathrm m$ each time, never leaving the line.
a) In how many ways can it reach point $B$, $5\,\mathrm m$ to the right of $A$, in exactly 7 jumps?
b) In how many ways can it reach point $C$, $5\,\mathrm m$ to the right of $A$, in exactly 9 jumps?
c) Can it reach point $D$ on the line at distance $2013\,\mathrm m$ from $A$ in exactly 2028 jumps? Justify.
a) In how many ways can it reach point $B$, $5\,\mathrm m$ to the right of $A$, in exactly 7 jumps?
b) In how many ways can it reach point $C$, $5\,\mathrm m$ to the right of $A$, in exactly 9 jumps?
c) Can it reach point $D$ on the line at distance $2013\,\mathrm m$ from $A$ in exactly 2028 jumps? Justify.