3.IN HOW MANY WAYS 3 BOYS AND 5 GIRLS BE ARRANGED IN A ROW SO THAT i)NO TWO BOYS R TOGETHER ii)ALL THE GILS ARE TOGETHER.(WITH EXPLANATION )

 

i) 5 girls can be seated in a row in ⁵P₅ = 5! ways.

Now, in the 6 gaps, 3 boys can be arranged in ⁶P₃ ways.

Hence, the number of ways in which no two boys sit together

= 5! x ⁶P₃ = 120 x 120 = 14400 ways

 

 

ii) Assume 5 girls to be together i.e. (one). Now there are 4 students.

Possible ways of arranging them are 4! ways

Now 5 girls can be arranged among themselves in 5! ways.

Thus, total no. of ways in which all girls are together = 4! x 5! = 24 x 120 = 2880