Question

A family of 4 brothers and 3 sisters is to be arranged in a row for a photograph. The number of ways in which they can seat if all the sisters are to sit together is:
A. 120
B. 240
C. 360
D. 720

Answer 1

Here this type of question is based on permutation and combination. Where we have to do an arrangement of 4 brothers and 3 sisters into a sequence or linear. We will make all sisters sit together so all sisters as one bundle so we can get 5 elements to be arranged.

Complete step-by-step solution:
It is given that there are 4 brothers and 3 sisters in a family.
According to the question we have to make all sisters sitting together.
For that, we count all sisters as one bundle.
Now we have a total of 5 places to arrange them.
So, we can arrange 4 brothers and 3 sisters in $5!$ ways.
But there are 3 sisters. We consider them as one bundle but we can arrange them inside.
We can arrange 3 sisters in $3!$ ways.
Now, the total arrangements of 4 brothers and 3 sisters in which all sisters are to sit together will be given by,
$\Rightarrow$ Total arrangements $= 5! \times 3!$
Expand the terms,
$\Rightarrow$ Total arrangements $= 5 \times 4 \times 3 \times 2 \times 1 \times 3 \times 2 \times 1$
Multiply the terms,
$\therefore$ Total arrangements $= 720$
Thus, the number of ways in which they can seat if all the sisters are to sit together is 720 ways.

Hence, option (D) is the correct answer.

Note: A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. Whenever they ask us to sit together there, we have to make one bundle of those elements. After arranging all elements together, we have to rearrange those elements which are inside that one bundle.