10
QuizMultiple Choice

Finding Outcomes — Quiz

Question 10 • Integrated Math II CR SUSD (EX)

Three out of seven students in the cafeteria line are chosen to answer survey questions. How many different combinations of three students are possible? sub 7 cap c sub 3 is equal to the fraction with numerator 7 factorial and denominator open paren 7 minus 3 close paren factorial 3 factorial

Answer
A
210
B
70
C
7
D
35

Explanation

Because the order of the three students does not matter, use combinations: 7 choose 3 = 7! ÷ (4! × 3!). Simplifying gives (7 × 6 × 5) ÷ (3 × 2 × 1) = 35, so 35 different groups are possible. The correct choice is C, 35.

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