Permutation-Combination
Aptitude

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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

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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 $= \textbf{71}$


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