Question

There are 8 students appearing in an examination of which 3 have to appear in a Mathematics paper and the remaining 5 in different subjects. In how many ways can they be made to sit in a row if the candidates In Mathematics cannot sit next to each other?

• A. 14400
• B. 16400
• C. 15400
• D. 17400

Answer 1

The correct option is A 14400

Total number of candidates = 8.
5 different subjects candidates can be seated in P(5, 5) = 5! ways.
In between 5 candidates there are six places for 8 Mathematics candidates.
$\therefore$ The Mathematics candidates can be seated in P(6, 3) ways
$\therefore$ By fundamental principle of counting:
The required number of ways = 5! $\times$ P (6, 3)
$=120\times \frac{6!}{3!}=120\times 6\times 5\times 4=14400.$