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# 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

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