Question

The numbers of arrangements of the letters of the word 'SALOON', if the two 'O's do not come together, is

• A. $360$
• B. $720$
• C. $240$
• D. $120$

Answer 1

The correct option is C $240$

Total no. of arrangements

possible for ${}^{\prime }SALOO{N}^{\prime }$

${=}^6{P}_2=\frac{6!}{2!}=6\times 5\times 4\times 3$

$=360$

No. of times '00' occur

together

$\underset{–}{00}\times \underset{–}{5}\times \underset{–}{4}\times \underset{–}{3}\times \underset{–}{2}=120$

$\therefore$ No. of times '00' do

not occur together

= Total outcomes - No. of times they occur together

$=360-120$

$=240$