AnswersGeometryProbability with Combinations and Permutations

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Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. Which expression represents the probability that both students chosen are sophomores?

A
the fraction with numerator sub 6 cap p sub 2 and denominator sub 20 cap p sub 2
B
the fraction with numerator open paren sub 20 cap p sub 6 close paren times open paren sub 19 cap p sub 5 close paren and denominator sub 20 cap p sub 2
C
the fraction with numerator 6 cap c sub 2 and denominator 20 cap c sub 2
D
the fraction with numerator open paren sub 20 cap c sub 6 close paren times open paren sub 19 cap c sub 5 close paren and denominator sub 20 cap c sub 2
4

A standard deck of 52 playing cards contains four of each numbered card 2 ce bond negative 10 and four each of aces, kings, queens, and jacks. Two cards are chosen from the deck at random. Which expression represents the probability of drawing a king and a queen?

A
the fraction with numerator open paren sub 4 cap c sub 1 close paren times open paren sub 3 cap c sub 1 close paren and denominator sub 52 cap c sub 2
B
the fraction with numerator open paren sub 4 cap p sub 1 close paren times open paren sub 4 cap p sub 1 close paren and denominator sub 52 cap p sub 2
C
the fraction with numerator open paren sub 4 cap c sub 1 close paren times open paren sub 4 cap c sub 1 close paren and denominator sub 52 cap c sub 2
D
the fraction with numerator open paren sub 4 cap p sub 1 close paren times open paren sub 3 cap p sub 1 close paren and denominator sub 52 cap p sub 2
8

At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives. Which expression represents the probability that a student chooses an art elective and a history elective?

A
the fraction with numerator sub 7 cap c sub 2 and denominator sub 12 cap c sub 2
B
the fraction with numerator open paren sub 3 cap p sub 1 close paren times open paren sub 4 cap p sub 1 close paren and denominator sub 12 cap p sub 2
C
the fraction with numerator open paren sub 3 cap c sub 1 close paren times open paren sub 4 cap c sub 1 close paren and denominator sub 12 cap c sub 2
D
the fraction with numerator sub 7 cap p sub 2 and denominator sub 12 cap p sub 2
10

The track team gives awards for first, second, and third place runners. There are 10 students from school cap A and 12 students from school cap b competing. Which expression represents the probability that all three awards will go to a student from school cap b ?

A
the fraction with numerator sub 12 cap p sub 3 and denominator sub 22 cap p sub 3
B
the fraction with numerator sub 22 cap p sub 3 and denominator sub 22 cap p sub 12
C
the fraction with numerator sub 22 cap c sub 3 and denominator sub 22 cap c sub 12
D
the fraction with numerator sub 12 cap c sub 3 and denominator sub 22 cap c sub 3

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