Solve the problem.
-If 3 boys and 2 girls are arranged at random in a row, what is the probability that two boys will not be in adjacent seats?
A) $\frac { 12 } { 5 ! }$
B) $\frac { 3 } { 5 ! }$
C) $\frac { 2 } { 5 }$
D) $\frac { 2 ! } { 5 ! }$

Question

Solve the problem.
-If 3 boys and 2 girls are arranged at random in a row, what is the probability that two boys will not be in adjacent seats? 
A) $\frac { 12 } { 5 ! }$
B) $\frac { 3 } { 5 ! }$
C) $\frac { 2 } { 5 }$
D) $\frac { 2 ! } { 5 ! }$

Quizplus · Accepted Answer

To ensure two boys are not adjacent, we can first place the 2 girls and then insert the 3 boys in the spaces between and on the sides of the girls. There are 3 spaces (before the first girl, between the two girls, and after the second girl) where the 3 boys can be placed, which can be done in 3! ways. The girls can be arranged in 2! ways. Thus, the total number of favorable arrangements is 3! * 2!. The total number of ways to arrange 3 boys and 2 girls without restrictions is 5!. Therefore, the probability is $\frac{3! * 2!}{5!} = \frac{12}{5!}$.

Solve the Problem 125!\frac { 12 } { 5 ! }5!12​

Solve the Problem $\frac { 12 } { 5 ! }$