Question

Four sisters and two brothers are arranged in different ways in a straight line for several photographs to be taken .how many different arrangements are possible if
a) there are no restrictions
b)the two brothers must be seperated
c) the two brothers stand on either end

Answer 1

Answer:

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Answer 2

Answer:

No.of sisters = 4

No. of brothers = 2

Total no. of people = 6

Number of arrangements of 6 people = 6!

                                                               = 720

Now we are supposed to find the two brothers must be separated other.

We need to fix the place of two brothers

Number of arrangements with two brothers next to each other = $5! \times 2!=240$

Number of arrangements with the two brothers separated = 720 – 240

                                                                                                  = 480

We are supposed to find the two brothers stand on either end

Since two brothers are fixed so arrangement will be done among 4 sisters

Number of arrangements with two brothers stand on either end = $4! = 24$