Question

Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8? if.

(i) repetitions of digits is allowed

(ii) repetitions of digits is not allowed.

Answer 1

(i) Number of digit given = 4 (2,4, 6, 8) 

So the unit place can be filled in 4 ways, 10’s place can be filled in 4 ways and 100’s place can be filled in 4 ways 

∴ The unit place, 10’s place and 100’s place together can be filled (i.e) So the Number of 3 digit numbers = 4 × 4 × 4 = 64 ways

(ii) The unit place can be filled (using the 4 digits) in 4 ways after filling the unit place since repetition of digits is not allowed that digit should be excluded. So the 10’s place can be filled in (4 – 1) 3 ways and the 100’s place can be filled in (3 – 1) 2 ways 

So the unit place, 10’s and 100’s places together can be filled in 4 × 3 × 2 = 24 ways 

(i.e) The number of 3 digit numbers = 4 × 3 × 2 = 24 ways