Question

In how many ways can $10$ maths teachers and $4$ science teachers be seated at a round table if all the $4$ science teachers do not sit together

• A. $13!\times 4!$
• B. $13!$
• C. $13!-(10!\times 4!)$
• D. $10!\times 4!$

Answer 1

The correct option is C $13!-(10!\times 4!)$

Consider $4$ science teachers as an identity.

Therefore $10+1=11$

$11$ units are there .

Number of circular arrangement $=(11-1)!=10!$

Science teachers can arrange among themselves in $10!\times 4!$

Number of ways (all the 4 science teachers do not sit together ) $=$ Total possible arrangements $-$ Arrangements when science teachers are together.

$=13!-(10!\times 4!)$