four girls and six boys are in a spanish club. three of the people will be chosen at random to represent the…

Explanation:

Step1: Calculate total number of people

There are 4 girls and 6 boys, so $4 + 6=10$ people in total. The number of ways to choose 3 people out of 10 is given by the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 10$ and $r=3$. So $C(10,3)=\frac{10!}{3!(10 - 3)!}=\frac{10\times9\times8}{3\times2\times1}=120$.

Step2: Calculate number of ways to choose 1 girl and 2 boys

The number of ways to choose 1 girl out of 4 is $C(4,1)=\frac{4!}{1!(4 - 1)!}=\frac{4!}{1!3!}=4$. The number of ways to choose 2 boys out of 6 is $C(6,2)=\frac{6!}{2!(6 - 2)!}=\frac{6\times5}{2\times1}=15$. By the multiplication - principle, the number of ways to choose 1 girl and 2 boys is $C(4,1)\times C(6,2)=4\times15 = 60$.

Step3: Calculate the probability

The probability $P$ that 1 girl and 2 boys are chosen is the number of favorable outcomes divided by the number of total outcomes. So $P=\frac{60}{120}=0.5 = 50%$.

Answer:

50%