Question

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?​

Answer 1

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(i)

"Repetition of the digits is allowed"

The first , second and third place can be filled in 5 ways by anyone of 1, 2, 3, 4 and 5 digits

By multiplication principle ,

Number of ways = 5 × 5 × 5 = 125 ways

(ii)

"Repetition of the digits is not allowed"

The first place can be filled in 5 different ways by anyone of 1, 2, 3, 4 and 5 digits

The second place can be filled in 4 different ways by anyone of the remaining digits

The third place can be filled in 3 different ways by anyone of the remaining digits

By multiplication principle ,

Number of ways = 5 × 4 × 3 = 60 ways