Question

Number of selection of 6 different letters that cab be made from the words 'SUMAN' and 'DIVYA' so that each selection contains 3 letters from each word, is

• A. 64
• B. 84
• C. 100
• D. 106

Answer 1

The correct option is A 64

Selecting $3$ letters from both words in ${{}^{5}C}_3\times {{}^{5}C}_3$ ways but negating cases where $A$ is selected in both $={{}^{4}C}_2\times {{}^{4}C}_2=6\times 6=36$

$\Rightarrow$ selections is ${\left({{}^{5}C}_3\right)}^2-36$ ways

$=(10\times 10)-36=64$ ways