Question

There is an international cricket match series between India and Australia of $9$ matches. The number of ways in which the series can be won by India such that there is exactly one draw in the whole series is

Answer 1

When India wins $5$ matches out of $9$
Number of ways $=\frac{9!}{5!3!1!}=504$

When India wins $6$ matches out of $9$
Number of ways $=\frac{9!}{6!2!1!}=252$

When India wins $7$ matches out of $9$
​​​​​​​Number of ways $=\frac{9!}{7!1!1!}=72$

When India wins rest all $8$ matches out of $9$
​​​​​​​​​​​​​​Number of ways $=\frac{9!}{8!1!}=9$

Total ways $=504+252+72+9=837$