3
lesson pretestMultiple Choice

Pretest

Question 3 • Mathematics II

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
70
B
210
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.

AI-written and checked against the verified answer.

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