Two families with three members each and one | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the three families be $F_1, F_2,$ and $F_3$. The number of members in these families are $3, 3,$ and $4$ respectively.Since the members of the

Vedclass · Accepted Answer

$(3!)^2 \cdot 4! \cdot 3!$

Vedclass · Answer

(B) Let the three families be $F_1, F_2,$ and $F_3$. The number of members in these families are $3, 3,$ and $4$ respectively.Since the members of the same family must stay together,we can treat each family as a single unit.There are $3$ such units (families) which can be arranged among themselves in $3!$ ways.Within each family,the members can be arranged among themselves:- Family $1$ ($3$ members) can be arranged in $3!$ ways.- Family $2$ ($3$ members) can be arranged in $3!$ ways.- Family $3$ ($4$ members) can be arranged in $4!$ ways.Therefore,the total number of ways is $3! 	imes (3! 	imes 3! 	imes 4!) = (3!)^2 	imes 3! 	imes 4! = 6 	imes (3!)^2 	imes 4!$.However,looking at the provided options,the expression $(3!)^2 \cdot 3! \cdot 4!$ simplifies to $6 \cdot (3!)^2 \cdot 4!$. Given the structure of the options,the correct arrangement is $3! \cdot 3! \cdot 3! \cdot 4!$.

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 members of the same family are not separated?

Similar Questions

The number of ways in which the letters of the word $ARRANGE$ can be arranged such that both $R$ do not come together is

Ten chairs are numbered as $1$ to $10$. Three women and two men wish to occupy one chair each. First,the women choose the chairs marked $1$ to $6$,then the men choose the chairs from the remaining. The number of possible ways is

The number of different permutations that can be formed by taking $4$ letters at a time from the letters of the word '$REPETITION$' is

The number of seven-digit odd numbers that can be formed using all the seven digits $1, 2, 2, 2, 3, 3, 5$ is $.......$

The number of $5$-digit numbers which are divisible by $4$,with digits from the set $\{1, 2, 3, 4, 5\}$ and the repetition of digits is allowed,is . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module