A Hockey game is played between team Blue and Red. There are a total of 8 players in each team and 4 will play in the game. Rhea is in team blue and Vaishali in team Red. What is the probability that at least one of Rhea or Vaishali is in playing four?
Answer & explanation
Correct answer: option 2
Total number of ways to select team blue without any restriction = \(^8 \mathrm{ C }_4\)
Similarly team Red can be selected in \(^8 \mathrm{ C }_4\) ways
Total number of ways to select both the teams = \(^8 \mathrm{ C }_4 \times ^8 \mathrm{ C }_4\)
P (at least one of them plays) =1 – P (none of them plays)
Total number of ways of selecting team without selecting Rhea and vaishali
= \(^7 \mathrm{ C }_4 \times ^7\mathrm{ C }_4\)
P (at least one of them plays)= 1 – \(\frac{^7 \mathrm{ C }_4 \times ^7 \mathrm{ C }_4}{^8 \mathrm{ C }_4 \times ^8 \mathrm{ C }_4}\)
= 1- \(\frac{1}{4}\) =\(\frac{3}{4}\)
Hence, option B is correct.