Class XI Chapter 7 – Permutation and Combination Maths ______________________________________________________________________________ Question 3: Compute 8! 6! 2! Solution 3: 8! 876! 87 28 6! 2! 6! 21 2 Question 4: If 1 1 x 6! 7! 8! Solution 4: 1 1 x 6! 7! 8! , find x. 1 1 x 6! 7 6! 8 7 6! 1 1 x 1 6! 7 876! 1 x 1 7 8 7 8 x 7 8 7 887 x 7 x 64 Question 5: Evaluate (i) n! n r ! n6, r 2 Solution 5: , when (ii) n9, r 5 n! 6! 6! 654! (i) When n 6, r 2: 30 nr ! 6 2 ! 4! 4! Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 7 – Permutation and Combination Maths ______________________________________________________________________________ (ii) When n! 9! 9! 987654! n 9, r 5: ! 9 5 ! 4! 4! nr 98765 15120 Exercise 7.3 Question 1: How many 3-digit numbers can be formed by using the digits 1 to 9 if no digits is repeated? Solution 1: 3-digit numbers have to be formed using the digits 1 to 9. Here, the order of the digits matters. Therefore, there will be as many 3-digit numbers as there are permutations of 9 different digits taken 3 at a time. Therefore, required number of 3-digit numbers 9876! 987 504 6! 9 P3 9! 9! 9 3 ! 6! Question 2: How many 4-digit numbers are there with no digit repeated? Solution 2: The thousands place of the 4-digit number is to be filled with any of the digits from 1 to 9 as the digit 0 cannot be included. Therefore, the number of ways in which thousands place can be filled is 9. The hundreds, tens, and units place can be filled by any of the digits from 0 to 9. However, the digits cannot be repeated in the 4-digit numbers and thousands place is already occupied with a digit. The hundreds, tens, and units place is to be filled by the remaining 9 digits. Therefore, there will be as many such 3-digit numbers as there are permutations of 9 different digits taken 3 at a time. Number of such 3-digit numbers 9876! 98 7 504 6! 9 P3 9! 9! 9 3 ! 6! Thus, by multiplication principle, the required number of 4-digit numbers is 9504 4536 . Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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