Question

How many numbers can be formed taking $4$ digits form digits $1,1,2,3,4,5,6$ whereas digit $4$ and $5$ are compulsory ?

Answer 1

Total number of digits=$6$
We Have to take $4$ digits but digit $4$ and $5$ are compulsory.
Thus, we have to choose only $2$ digits out of $6-2=4$ digits.
Now, the numbers formed by using $4$ digits is ${}^4{P}_4.$
Hence required number
=${}^4{C}_2{\times }^4{P}_4$
=$\frac{4\times 3}{2\times 1}\times 4!$
= $6\times 24=144$