Aptitude 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 $= \textbf{71}$