Question

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?

Class X1 - Maths -Permutations and Combinations Page 138

Answer 1

(i) when repetition of digits are allowed .
given,
1, 2 , 3 , 4, 5 . since there are five digits
Therefore , number of ways to fill each place of 3 digit number are 5
Hence,
by Fundamental principle of counting,
total number of ways = 5 × 5 × 5 = 125

(ii) when repetition isn't allowed.
here, five digits are available .
therefore,
number of ways to fill the unit place = 5
number of ways to fill tenth place = 4
number of ways to fill hundred place = 3
hence,
by Fundamental principle of counting,
total number of ways = 5 × 4 × 3 = 60