Combinatorics | Number Theory Answers

25 students of your school participated in a tournament of three games namely : cricket, football & basket ball. 15 students received medals in cricket, 12 in football, 11 in basketball, 5 in cricket and basket ball, 9 in cricket & football, 4 in football & basketball and 3 in all the three games. How many students received medals in (i) None of the games (ii) cricket only.

There are 15 boys and 10 girls in your class. A four member committee is to be formed from the students
of your class. In how many ways this can be done if the committee consists at least three girls?

Q. what is the result of 0 power of o ?

How many words can we build using exactly 5 A's, 5 B's and 5 C's if the first 5 letters cannot be A's, the second 5 letters cannot be B's and the third 5 letters cannot be C's? Hint: Group the different ways according to the number of B's in the first group.

Find the number of three digits numbers from 100 to 999 inclusive which have any one digit that is the average of the other two.

5 balls are to be placed in 3 boxes. Each box can hold all 5 balls. In how many different ways can we place the balls so that no box remains empty if, (i) balls & boxes are different (iii) balls are different but boxes are identical (ii) balls are identical but boxes are different (iv) balls as well as boxes are identical

How many 15 letter arrangements of 5 A's, 5 B's and 5 C's have no A's in the first 5 letters, no B's in the next 5 letters, and no C's in the last 5 letters.

For each positive integer k, let Sk denote the increasing arithmetic sequence of integers whose first term is 1 and whose common difference is k. For example, S3 is the sequence 1, 4, 7, 10...... Find the number of values of k for which Sk contain the term 361

Total numbers of words , taking all letters at a time ,such that at least one repeating letter is at odd positionin each word is given by(in word MATHEMATICS)