# Moderate Permutation-Combination Solved QuestionAptitude Discussion

 Q. In a cricket match if a batsman score $0,1,2,3,4$ or $6$ runs of a ball, then find the number or different sequences in which he can score exactly 30 runs of an over. Assume that an over consists of only 6 balls and there were no extra and no run outs.
 ✖ A. 86 ✔ B. 71 ✖ C. 56 ✖ D. 65

Solution:
Option(B) is correct

Case A:

Five 6 and one 'zero',

$= \dfrac{6!}{5!}$

$= 6$

Case B:

our 6 and one '2' and one '4':

$=\dfrac{6!}{4!}$

$= 30$

Case C:

Three 6 and three '4',

$= \dfrac{6!}{3!×3!}$

$= 20$

Case D:

Four 6 and two '3',

$= \dfrac{6!}{4!×2!}$

$= 15$

Total number of different sequences $= \textbf{71}$