There are 777 students in a class: 555 boys and 222 girls. if the teacher picks a group of 444 at random, what is the probability that everyone in the group is a boy?

The probability is 0.1429.

The probability that the first person chosen is a boy is 5/7. The probability that the second is a boy is 4/6; the third, 3/5; and the fourth, 2/4. Both the numerator and denominator decrease every time, because you lose a boy to choose from and you lose a student to choose from as well. This gives us:

5/7 (4/6) (3/5) (2/4) = 120/840 = 0.1429.