Class 11

Math

Algebra

Permutations and Combinations

A four digit number is called a doublet if any of its digit is the same as only one neighbour. For example, $1221$ is a doublet but $1222$ is not. Number of such doublets are :

- $2259$
- $2268$
- $2277$
- $2349$

Number of ways$=9_{3}$ Ways

Case: 2 $bbac$

Number of ways$=9_{3}$ Ways

Case: 3 $acdd$

Number of ways$=9_{3}$ Ways

Case: 4 $aabb$

Number of ways$=9_{2}$ Ways

Total number of ways

$=9_{3}×3×9_{2}$

$=2268$ Ways