Question

In how many can 4 boys and 3 girls sit in a row if two boys sit always together. <br />This question from permutations<br />Ans - 1440

Answer 1

Hey MATE!

We have 4 boys and 3 girls arranged in a row such that no two girls are adjacent.

I would first start off with arranging/seating the boys . 4 boys can be seated in 4!ways. Thus 4 boys can be seated in 4!=4∗3∗2∗1=24 ways.

{Note: Order matters here. i.e. Seating arrangement of B1 B2 B3 B4 is different from B1 B3 B2 B4, where, B1,B2,B3,B4 are four different boys.}

So, this is a permutation and so 4 boys can be arranged in 4 places in 4P4 ways= 4!(4−4)!=4!0!=24. Thus the boys can be arranged in 4! = 24 ways. {Note: 0!=1}

Now we have to place/arrange the girls such that no two girls are adjacent. So we can arrange them in 5 different places as shown below.

_B_B_B_B_

The first girl can be seated in any of the 5 places.

The second girl can be seated in any of the remaining 4 places.

The third girl can be seated in any of the remaining 3 places.

So, the number of ways that the girls can be seated: 5∗4∗3=60

This can also be done as follows: There are 5 places available for 3 girls to be seated and the order of seating matters. Thus the 3 girls can be seated in 5 places in 5P3 ways = 5!(5−3)!=5!2!=60

The total number of ways that 4 boys and 3 girls can be arranged in a row such that no two girls are adjacent : 4P4∗5P3=24∗60=1440 ways.

Hope it helps

Hakuna Matata :))