Surekha typed a 6-digit number but the two 3's she typed did not show. What appeared instead was 7007. How many different 6-digit numbers can be there?

Given:

Surekha typed a 6-digit number but the two 3's she typed did not show. What appeared instead was 7007.

Calculation:

In the number 7007 if we need to fit two more digits not placed adjacent to each other, then we have the following options

⇒ _7_0_0_7_

Number of ways to place two 3's in 5 gaps = ⁵C₂ = 10

If the two digits are to be placed together, then we have the following options

⇒  __7__0__0__7__

Number of ways to place the pair of 3's in 5 gaps = ⁵C₁ = 5

Now, the number of different 6-digit numbers = 10 + 5

⇒ 15

∴ There can be 15 different 6-digit numbers.