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 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?