Twenty teams have entered a tournament. In order to reduce the number of teams to eight, they are put into groups of five and the teams in each group play each other twice. The top two teams in each group progress to the next round. From this point on, teams are paired up, playing each other once with the losing team being eliminated. How many games are played during the whole tournament?
Important Questions on Permutations and Combinations
A bank provides each account holder with a nine-digit card number that is arranged in three blocks, as shown in the example opposite. Find, in index form, the number of card numbers available if:
there are no restrictions on the digits used
A bank provides each account holder with a nine-digit card number that is arranged in three blocks, as shown in the example opposite. Find, in index form, the number of card numbers available if:
none of the three blocks can begin with
A bank provides each account holder with a nine-digit card number that is arranged in three blocks, as shown in the example opposite. Find, in index form, the number of card numbers available if:
the two digits in the second block must not be the same
A bank provides each account holder with a nine-digit card number that is arranged in three blocks, as shown in the example opposite. Find, in index form, the number of card numbers available if:
the three-, two- and four-digit numbers on the card are even, odd and even, respectively.
A bakery wishes to display seven of its types of cake in a row in its shop window. There are six types of sponge cake, five types of cheesecake and three types of fruitcake. Find the number of possible displays that can be made if the bakery places:
a sponge cake at each end of the row and includes no fruitcakes in the display
A bakery wishes to display seven of its types of cake in a row in its shop window. There are six types of sponge cake, five types of cheesecake and three types of fruitcake. Find the number of possible displays that can be made if the bakery places:
a fruitcake at one end of the row with sponge cakes and cheesecakes placed alternately in the remainder of the row.
