A batsman scores exactly a century by hitting fours and sixes in t | Filo
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Class 11

Math

Algebra

Permutations and Combinations

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A batsman scores exactly a century by hitting fours and sixes in twenty consecutive balls. In how many different ways can he do it if some balls may not yield runs and the order of boundaries and Over boundaries are taken into account?

Solution: Let the batsman hit fours, sixes and let balls may not yield runs. Then we have,

Where

From Eqs. (1) and (2),




Hence, can be as any of cannot exceed . So, we have following type of distribution of runs:
Number of fours, Number of sixes, Number of zeros, Number of ways of arranging and
Hence, the total number of ways is
.
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