In the next World Cup of cricket there will be 12 teams, divided equally in two groups. Teams of each group will play a match against each other. From each group 3 top teams will qualify for the next round. In this round each team will play against others once. Four top teams of this round will qualify for the semifinal round, where each team will play against the others once. Two top teams of this round will go to the final round, where they will play the best of three matches. The minimum number of matches in the next World Cup will be
A.
54
B.
53
C.
38
D.
None of these
Answer :
53
Solution :
The number of matches in the first round $$ = {\,^6}{C_2} + {\,^6}{C_2}.$$
The number of matches in the next round $$ = {\,^6}{C_2}.$$
The number of matches in the semifinal round $$ = {\,^4}{C_2}.$$
∴ the required number of matches $$ = {\,^6}{C_2} + {\,^6}{C_2}{ + ^6}{C_2}{ + ^4}{C_2} + 2.$$ Note : For “best of three” at least two matches are played.
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is