Question

PLEASE Help me solve this combinatorics question-

Q-Tanya typed a six-digit number, but the two 1's she typed did not show. What appeared was 2006. Find the number of different 6-digit numbers she would have typed.​

Answer 1

Given:

Number of digits in the number = 6

The number typed = 2006

The numbers left = two 1's

To find:

The number of different 6-digit numbers she would have typed.

Solution:

In the number 2006 if we need to fit two more digits not placed adjacent to each other, then we have following options:

_2_0_0_6_

Number of ways to select two blanks from 5 blanks = 5C2 = 10

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

__2__0__0__6__

Number of ways to select a pair of blank from 5 of them = 5C1 = 5

Total number of different words= 10*5 = 50

Therefore the required answer is 50.