In a group of 30 students, 18 girls and 12 boys, a leadership team of 4 students is chosen. What is the probability of having all girls in the President's leadership team?

The total number of ways to choose the leadership team of 4 students from 30 is given by the combination formula:

\text{Total ways to choose team} = \binom{30}{4}

Since we want the President's team to be all girls, we need to choose all 4 girls out of the 18 available. The number of ways to choose 4 girls from 18 is:

\text{Ways to choose all girls} = \binom{18}{4}

The probability of having all girls in the President's leadership team is then:

P(\text{All girls}) = \frac{\text{Ways to choose all girls}}{\text{Total ways to choose team}}

Plugging in the values:

P(\text{All girls}) = \frac{\binom{18}{4}}{\binom{30}{4}}

P(\text{All girls}) = \frac{\frac{18!}{4!(18-4)!}}{\frac{30!}{4!(30-4)!}}

P(\text{All girls}) = \frac{\frac{18!}{4!14!}}{\frac{30!}{4!26!}}

P(\text{All girls}) = \frac{\frac{18*17*16*15}{4*3*2*1}}{\frac{30*29*28*27}{4*3*2*1}}

P(\text{All girls}) = \frac{18*17*16*15}{30*29*28*27}

\boxed{P(\text{All girls})=0.111658}