Team A which consists of 6 players wishes to have badminton matches with team B which consists of 7 players. Calculate the number of different single matches that can be held.

Calculate the number of ways how 4 different prizes can be given to 4 participants of a quiz.

Calculate the number of ways to arrange 9 books of different tittles on a book rack.

Using the digits 3, 4, 5, 6 and 7, without repetitions, calculate the number of four- digit numbers that are greater than 5000 that can be formed

A group of 4 men and 3 ladies are to be seated in a row for a photo session. If the men and ladies want to be seated alternately, calculate the number of different arrangements

Atiff has 6 durians , 5 papaya and 2 apples. If he wants to arrange these fruits of the same kind have to be grouped together , calculate the numbers of different arrangements. The sizes of the fruits are different.

The diagram shows nine letters, find the total number of different arrangements of all the letters if the letters "E" and "S" are to be adjacent to each other

A code is to be formed using A, B, C , D, E, F, 5, 6, 7 and 8. If the code must consists of 4 letters followed by 3 digits numbers, how many codes can be formed without repetition

Find the number of ways the word "EIGHT" can be arranged if the vowels must always be side by side.