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 $SUMAN$ and $DIVYA$ 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 $N^2=64\Rightarrow N=8$