From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition, including at least 4 boys.and 4 girls. The two girls who won the prizes last year should be included. In how many ways can the selection be made?

In a class there are 25 boys and 10 girls. The teacher wants to select 1 boy and 1 girl to represent the class in-a function. In how many ways can the teacher make the selection

In a class there are 30 students and 33 (1)/(3) % of them are girls. How many girls are in the class?

A word consists of 9 letters: 5 consonents and 4 vowels. Three letters are chosen at random. In how many ways can these 3 letters be chosen.

In an examination a question paper consists of' 12 questions divided into 2 parts I and II containing 5 and 7 questions respectively. A student is required to attempt 8 questions. In how many ways he can select 3 questions from part I and 5 questions from part II?

In an examination a question paper consists of' 12 questions divided into 2 parts I and II containing 5 and 7 questions respectively. A student is required to attempt 8 questions. In how many ways the student can select 5 questions from part I and 3 questions from part II.

In an examination a question paper consists of' 12 questions divided into 2 parts I and H containing 5 and 7 questions respectively. A student is required to attempt 8 questions. In how many ways the student can answer 8 questions by selecting at least 3 questions from each part.

In an examination a question paper consists of' 12 questions divided into 2 parts I and II containing 5 and 7 questions respectively. A student is required to attempt 8 questions. In how many ways the student can select 4 questions from part I and 4 questions from part II.

A student has to answer 6 out of 10 questions which are divided into two parts containing 5 questions each and he is permitted to attempt not mom than 4 from any group. In how many ways can he make up his choice?

A team of 11 cricket players is to be chosen from 15 players. In how many ways can this be done so as to: Include A and exclude B.