Question:
Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?
Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?
Show Hint
Treat each family as one block, arrange the 3 blocks, then arrange the members inside each block.
Updated On: Nov 5, 2026
- \(2!\,3!\,4!\)
- \((3!)^3\cdot(4!)\)
- \(3!\,(4!)^3\)
- \((3!)^2\cdot(4!)\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Each family must sit together, so treat each family as a single block.
Number of ways to arrange the 3 blocks in a row = \(3!\).
Arrangements inside the blocks: \(3!\) for the first 3-member family, \(3!\) for the second 3-member family, \(4!\) for the 4-member family.
Total = \(3!\times 3!\times 3!\times 4!=(3!)^3\cdot(4!)\).
Answer: (2) \((3!)^3\cdot(4!)\)
Number of ways to arrange the 3 blocks in a row = \(3!\).
Arrangements inside the blocks: \(3!\) for the first 3-member family, \(3!\) for the second 3-member family, \(4!\) for the 4-member family.
Total = \(3!\times 3!\times 3!\times 4!=(3!)^3\cdot(4!)\).
Answer: (2) \((3!)^3\cdot(4!)\)
Was this answer helpful?
0
0
Top JEE Main Mathematics Questions
- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
- If , then the general value of is:
- The general solution of
- If the constant term in the binomial expansion of $\left(\frac{x^{\frac{3}{2}}}{2}-\frac{4}{x^l}\right)^9$ is $-84$ and the coefficient of $x^{-3 l}$ is $2^\alpha \beta$, where $\beta<0$ is an odd number, then $|\alpha l-\beta|$ is equal to_____
View More Questions
Top JEE Main permutations and combinations Questions
- The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is______
- Five people are distributed in four identical rooms. A room can also contain zero people. Find the number of ways to distribute them.
- The number of ways to distribute the 21 identical apples to three children’s so that each child gets at least 2 apples.
- Let \( \alpha = \frac{(4!)!}{(4!)^{3!}} \) and \( \beta = \frac{(5!)!}{(5!)^{4!}} \). Then:
- Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to
View More Questions
Top JEE Main Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
View More Questions