Using the digits 0, 1, 2, 2, 3 how many numbers greater than 20000 can be made?

For the number to be greater than 20000 there are only two possibility.

Case 1: When numbers start with 2.

5^th place will be fixed with 2.

Remaining four places can be filled in 4! ways now.

So total number of ways fir a number to start with 2 is 4! = 4× 3× 2× 1

= 24 ways

Case 2: When numbers start with 3.

5^th place will be fixed with 3.

Since number is repeating so we use the formula .

Here p₁= 2 as number 2 is repeated two times.

Now the remaining places can be filled in ways.

= 12 ways

So total ways = 24 + 12

= 36 ways