Question

The ways in which the time table for Monday be completed if there must be 5 lessons that day (Algebra, Geometry, Calculus,Trigonometry, Vectors) and Algebra and Geometry must not immediately follow each other are

• A. $72$
• B. $5!$
• C. $35!/2$
• D. $6!$

Answer 1

The correct option is A $72$

$\to$ Total no. of ways in which the time table can be made $=5!=120$
$\to$ No. of ways in which the time table can be made, such that Algebra and Trigonometry follow each other $=2!\times 4!=48$
$\to$ So, the no. of ways in which the time table can be made, such that Algebra and Trigonometry do not follow each other $=120-48=72$