Probability Practice Test 2

There are at least three packets of chips in the cup board.
∴ Total 10 packets in all.
∴ {Number of packets of chips, Number of packets of biscuits}
= {(3, 7) or (4, 6) or (5, 5) or (6, 4) or (7, 3) or (8, 2) or (9, 1) or (10, 0)}
The number of ways in which three packets of chips can be drawn
${=}^3{\mathit{C}}_3{+}^4{\mathit{C}}_3{+}^5{\mathit{C}}_3$ ${+}^6{\mathit{C}}_3{+}^7{\mathit{C}}_3{+}^8{\mathit{C}}_3$ ${+}^9{\mathit{C}}_3{+}^{10}{\mathit{C}}_3$ = 330
The number of ways in which three packets of can be drawn when there are 9 packets of chips ${=}^9{\mathit{C}}_3=\frac{9!}{3!\left(9-3\right)!}=84$
∴ Required probability $=\frac{84}{330}=\frac{14}{55}$