Permutations and Combinations
Gap Method
JEE Main 2019
Grade 11
Question:
The number of ways in which $5$ boys and $3$ girls can be seated in a row so that no two girls sit together is:
(1) $14400$
(2) $14200$
(3) $12000$
(4) $10800$
Step-by-Step Solution
Key Concept: Seat 5 boys first: $5! = 120$ ways creating 6 gaps. Place 3 girls in 3 of the 6 gaps (order matters): $P(6, 3) = 6 \times 5 \times 4 = 120$. Total $= 120 \times 120 = 14400$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)