How many 3-digit numbers above 600 can be formed by using the digits 2

1.	How many 3-digit numbers above 600 can be formed by using the digits 2, 3, 4, 5, 6, if repetition of digits is allowed?
Answer» Given: We have 5 digits i.e. 2,3,4,5,6 To Find: Number of 3-digit numbers Condition: (i) Number should be greater than 600 (ii) Repetition of digits is allowed For forming a 3 digit number, we have to fill 3 vacant spaces. But as the number should be above 600, hence the first place must be occupied with 6 only because no other number is greater than 6. Let us represent the 3-digit number So the first place is filled with 6 = 1 ways Second place can be filled with 5 numbers = 5 ways Third place can be filled with 5 numbers = 5 ways Total number of ways = 1 × 5 × 5 = 25 Total number of 3-digit numbers above 600 which can be formed by using the digits 2, 3, 4, 5, 6 with repetition allowed is 25

How many 3-digit numbers above 600 can be formed by using the digits 2, 3, 4, 5, 6, if repetition of digits is allowed?

Answer»

Given: We have 5 digits i.e. 2,3,4,5,6

To Find: Number of 3-digit numbers

Condition: (i) Number should be greater than 600

(ii) Repetition of digits is allowed

For forming a 3 digit number, we have to fill 3 vacant spaces.

But as the number should be above 600, hence the first place must be occupied with 6 only because no other number is greater than 6.

Let us represent the 3-digit number

So the first place is filled with 6 = 1 ways

Second place can be filled with 5 numbers = 5 ways

Third place can be filled with 5 numbers = 5 ways

Total number of ways = 1 × 5 × 5 = 25

Total number of 3-digit numbers above 600 which can be formed by using the digits 2, 3, 4, 5, 6 with repetition allowed is 25