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# Lecture - 2 Chapter 7 Permutations and Combinations

NCERT Exercise 7.3 |

Meaning of Permutations, Derivation for rule of Permutations

**Question 1. **How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

**Question 2. **How many 4-digit numbers are there with no digit repeated?

**Question 3. **How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?

**Question 4. **Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?

**Question 5. **From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person can not hold more than one position?

**Question 6. **Find *n *if \( ^{n-1}P_3 : ^nP_4 = 1 : 9\)

**Question 7. **Find *r* if **(i)** \( ^5P_r = 2 ^6P_{r-1}\)**(ii)** \( ^5P_r = ^6P_{r-1}\)

**Question 8. **How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?

**Question 9. **How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if. **(i)** 4 letters are used at a time, **(ii)** all letters are used at a time, **(iii)** all letters are used but first letter is a vowel?