Question

Different words are being formed by arranging the letters of word 'SUCCESS'.
The number of words in which the consonants appear in alphabetical order is

• A. 42
• B. 40
• C. 420
• D. 280

Answer 1

Answer: (A)

Since, the consonants have to appear in alphabetical order, we have
$XCXCXSXSXSX$
Case I $U$ and $E$ are together
Number of words $={}^6{C}_1\times 2!=12$
Case II $U$ and $E$ are separated.
Number of words $={}^6{C}_2\times 2!=\frac{6\times 5}{2\times 1}\times 2=30$
$\therefore$ Required number of words $=30+12=42$