Question

If number of selections of $6$ different letters that can be made from the words 'SUMAN' and 'DIVYA' so that each selection contains $3$ letters from each word, is $N^2$ then the value of $N$ is

Answer 1

Here $A$ is common letter in words ${}^{\prime }SUMA{N}^{\prime }$ and $DIVY{A}^{\prime }$
Now for selecting six different letters we must select $A$ either from word 'SUMAN' or from word 'DIVYA'.
Hence for possible selections, we have
A excluded from $SUMAN+A$ included in SUMAN
${=}^4{C}_3{\cdot }^5{C}_3{+}^4{C}_2{\cdot }^4{C}_3=40+24=64$
Hence $N^2=64\Rightarrow N=8$.