Count the number of three-digit numbers which can be formed from the d

1.	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» (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

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»

(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

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