Question

The number of words, with or without meaning, that can be formed by taking $4$ letters at a time from the letters of the word ${}^{\prime }{\text{SYLLABUS}}^{\prime }$ such that two letters are distinct and two letters are alike, is

Answer 1

$SS,Y,LL,A,B,U$
$ABCC$ type words
$=\underset{\text{selection of}\text{2 alike letters}}{\underset{}{{}^2{C}_1}}\times \underset{\text{selection of}\text{2 distinct letters}}{\underset{}{{}^2{C}_1}}\times \underset{\text{arrangement of}\text{selected letters}}{\underset{}{\frac{4!}{2!}}}$
$=240$