2
QuizMultiple Choice

Permutations and Combinations

Question 2 • HCISD-Mathematical Models with Applications B-CR SUMMER

The governor is making a visit to your school and you need to assign seating for 14 students. Unfortunately there are only six seats in the front row. In how many different ways can you select and arrange the six lucky students?

Answer
A
2,162,160 different ways
B
1 different way
C
84 different ways
D
20,160 different ways

Explanation

There are 14 choices for the first seat, then 13 for the second, and so on, with 9 choices for the sixth seat. Since the order matters because the students are assigned to particular seats, multiply: 14 × 13 × 12 × 11 × 10 × 9 = 2,162,160. The correct choice is 2,162,160 different ways.

AI-written and checked against the verified answer.

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