Question:
The number of ways in which 6 boys and 4 girls can be seated around a round table such that 2 special boys and a special girl never sit together is
The number of ways in which 6 boys and 4 girls can be seated around a round table such that 2 special boys and a special girl never sit together is
Show Hint
Total ways - Together = Not Together.
Updated On: Jun 19, 2026
- 332620
- 332540
- 332640
- 332520
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Concept
Total circular arrangements of $n$ people is $(n-1)!$.
Step 2: Analysis
Total arrangements of 10 people $= 9! = 362880$.
Let the 3 special people (2 boys, 1 girl) be one unit.
Arrangements where they are together $= (8-1)! \times 3! = 7! \times 6 = 5040 \times 6 = 30240$.
Step 3: Calculation
Ways where they are NOT together $= 362880 - 30240 = 332640$.
Step 4: Conclusion
Hence, the number of ways is 332640. Final Answer: (C)
Total circular arrangements of $n$ people is $(n-1)!$.
Step 2: Analysis
Total arrangements of 10 people $= 9! = 362880$.
Let the 3 special people (2 boys, 1 girl) be one unit.
Arrangements where they are together $= (8-1)! \times 3! = 7! \times 6 = 5040 \times 6 = 30240$.
Step 3: Calculation
Ways where they are NOT together $= 362880 - 30240 = 332640$.
Step 4: Conclusion
Hence, the number of ways is 332640. Final Answer: (C)
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET Permutations Questions
- The number of ways of distributing \( 500 \) dissimilar boxes equally among \( 50 \) persons is
Given, the function \( f(x) = \frac{a^x + a^{-x}}{2} \) (\( a > 2 \)), then \( f(x+y) + f(x-y) \) is equal to
- In how many ways can 5 people be arranged in a row?
- The feasible region for the constraints \( x - 2 \le y, x \ge y - 1, x \ge 2, y \le 4, x, y \ge 0 \), is
- The domain of the function $f(x) = {^{7-x}\text{P}_{x-1}$ is
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions