In how many ways can a student of XI class choose 5 subjects out of 9 available subjects if two subjects, English (core) and Hindi (core) are compulsory .

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

In how many ways can 4 prizes be distributed among 5 students, if no student gets all the prizes?

In how many ways can 5 members forming a committee out of 10 be selected so that : two particular members must not be included ?

In how many ways can 5 members forming a committee out of 10 be selected so that : two particular members must be included?

In how many ways can the following diagram be coloured subject to the following conditions ? No two adjacent regions receive the same colour .

In how many ways can 9 different books be distributed among three students if each receives atleast 2 books?

In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together ?

In how many ways can the following diagram be coloured subject to the following conditions ? Each of the smaller triangle is to be painted with one of the three colours, red, blue or green.

In how many ways can a team 11 players be formed out of 25 players, if 6 out of them are always to be included and 5 always to be excluded

In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?