Permutation Tes...

A tournament is arranged as per the following rules: in the beginning 16 teams are entered and divided in 2 groups of 8 teams each where the team in any group plays exactly once with all the teams in the same group. At the end of this round top four teams from each group advance to the next round in which two teams play each other and the losing teams goes out of the tournament. Then the winning teams play for semi finals and finally there is one final. The rules of the tournament are such that every match can result only in a win or a loss and not in a tie. 

A tournament is arranged as per the following rules: in the beginning 16 teams are entered and divided in 2 groups of 8 teams each where the team in any group plays exactly once with all the teams in the same group. At the end of this round top four teams from each group advance to the next round in which two teams play each other and the losing teams goes out of the tournament. Then the winning teams play for semi finals and finally there is one final. The rules of the tournament are such that every match can result only in a win or a loss and not in a tie. 

A tournament is arranged as per the following rules: in the beginning 16 teams are entered and divided in 2 groups of 8 teams each where the team in any group plays exactly once with all the teams in the same group. At the end of this round top four teams from each group advance to the next round in which two teams play each other and the losing teams goes out of the tournament. Then the winning teams play for semi finals and finally there is one final. The rules of the tournament are such that every match can result only in a win or a loss and not in a tie. 

Number of ways of distributing 'n' different things into 'r' different groups is equal to 'rn'  when blank groups are taken into account and is equal to rⁿ - ^rC₁(r - 1)ⁿ  +  ^rC₂ (r - 2)² - .....+ (-1)^{r - 1  r}C_{r - 1} when blank groups are not permitted. 

Number of ways of distributing 'n' different things into 'r' different groups is equal to 'rn'  when blank groups are taken into account and is equal to rⁿ - ^rC₁(r - 1)ⁿ  +  ^rC₂ (r - 2)² - .....+ (-1)^{r - 1  r}C_{r - 1} when blank groups are not permitted. 

A cricket team of 11 players is to be selected from 8 batsmans, 6 bowlers, 4 all rounder and 2 wicket keepers. Answer the following question based on the information given.

A cricket team of 11 players is to be selected from 8 batsmans, 6 bowlers, 4 all rounder and 2 wicket keepers. Answer the following question based on the information given.