Question

India and Sri Lanka play one day international series until one team wins $4$ matches.

No match ends in a draw.

The number of ways in which series can be won is:

• A. $35$
• B. $70$
• C. $40$
• D. None of these

Answer 1

The correct option is B

$70$

Explanation for the correct option:

Let us suppose ‘$I$’ represents India and ‘$S$’ represents Sri Lanka.

Now we can arrange $I$ and $S$ show the wins for India and Sri Lanka.

Let us take an example ,$ISSSS$.

It means the first match is won by India followed by four wins by Sri Lanka.

This is the one way in which the series can be won.

Now suppose Sri Lanka wins the series, then the last match is always won by Sri Lanka.

Wins of India wins of Sri Lanka no. of ways

$\begin{array}{ccc}0& 4& 1\\ 1& 4& {}^4{C}_3=4\\ 2& 4& {}^5{C}_3=10\\ 3& 4& {}^6{C}_3=20\end{array}$

Therefore, the total number of ways, Sri Lanka can win the series is

$1+4+10+20=35$

India can also win the series in the same number of ways.

Therefore, the total number of ways in which a series can be won is equal to $35\times 2=70$

Hence, option (B) is the correct answer.