# IIT Foundation Mathematics Problems on Permutation and Combination

Q.1. Each section in first year of plus two course has exactly 30 students. If there are 3 sections, in how many ways can a set of 3 student representatives be selected from each section?

Q.2. How many numbers are there between 100 and 1000 such that every digit is either 2 or 9?

Q.3. How many numbers greater than 5000 can be formed with the digits 3, 5, 7, 8, 9 no digit being repeated?

Q.4. How many 6-digit numbers can be formed from the digits 1, 2, 4, 5, 6, 7 (no digit being repeated) which are divisible by 5?

Q.5. Find the number of arrangements of the letters of the word ‘BANANA’ in which the two N’s do not appear adjacently.

Q.6. If the letters of the word ‘AGAIN’ be arranged in a dictionary, what is the fiftieth word?

Q.7. How many different words, each containing 2 vowels and 3 consonants, can be formed with 5 vowels and 17 consonants?

Q.8. Find the number of diagonals that can be drawn by joining the angular points of a heptagon

Q.9. In how many ways can 7 persons sit around a table so that all shall not have the same neighbours in any two arrangements.

Q.10. How many numbers each containing four digits can be formed, when a digit may be repeated any number of times?

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