How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that
(i) repetition of the digits is allowed?
(ii) repetition of the digits is not allowed?

Solution:

(i) When repetition of digits is allowed:
No. of ways of choosing first digit = 5
No. of ways of choosing second digit = 5
No. of ways of choosing third digit = 5
By fundamental counting principle,
Total possible number of ways = 5×5×5 = 125.

(ii) When repetition of digits is not allowed:
No. of ways of choosing first digit = 5
No. of ways of choosing second digit = 4
No. of ways of choosing to third digit = 3
By fundamental counting principle,
Total possible number of ways = 5×4×3 = 60

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.1 Question 1

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) repetition of the digits is allowed? (ii) repetition of the digits is not allowed?

Summary:

(i) Total number of 3 digit numbers formed when repetition is allowed = 125, (ii) Total number of 3 digit numbers formed when repetition is not allowed = 60