NCERT Solutions
Class 11 - Mathematics - Chapter 6: PERMUTATIONS AND COMBINATIONS

EXERCISE 6.3

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

How many 4-digit numbers are there with no digit repeated?

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

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?

From a committee of 8 persons, in how many ways can we choose a chairman and a vice-chairman assuming one person cannot hold more than one position?

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

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

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

How many words, with or without meaning, can be made from the letters of the word MONDAY, assuming that no letter is repeated?
(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?

In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?

In how many ways can the letters of the word PERMUTATIONS be arranged if the:
(i) words start with P and end with S,
(ii) vowels are all together,
(iii) there are always 4 letters between P and S?