A) If exactly 4 boys volunteer, what is the probability that the team is all boys or no boys?
"={1(1) \\over \\dfrac{10!}{4!(10-4)!}}+{1\\cdot\\dfrac{6!}{4!(6-4)!} \\over \\dfrac{10!}{4!(10-4)!}}="
"={1 \\over 210}+{15 \\over 210}={8 \\over 105}"
B) What is the probability that Student 1 and Student 2 are on the team?
"={1\\cdot\\dfrac{8!}{2!(8-2)!} \\over \\dfrac{10!}{4!(10-4)!}}={28 \\over 210}={2 \\over 15}"
C) With two teacher coaches, the team of four takes a picture (6 people in picture). What is the probability that the teachers are together in the picture?
Consider two teacher coaches as one unit.
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