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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?

Answer Answer: 27000

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

Answer Answer: 8

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

Answer Answer: 216

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?

Answer Answer: 120

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

Answer Answer: 40

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

Answer Answer: NAAIG

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

Answer Answer: 816000

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

Answer Answer: 14

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.

Answer Answer: 360

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

Answer Answer: 9000

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