The number of possible combinations of 14 objects taken 3 at a time will be 364. Then the correct option is A.
What are permutation and combination?
A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
Then the number of possible combinations of 14 objects taken 3 at a time will be given by the combination formula.
ⁿCₓ = n! / [(n - x)! x!]
We have n = 14 and x = 3. Then we have
¹⁴C₃ = 14! / [(14 - 3)! × 3!]
¹⁴C₃ = 14 × 13 × 12 × 11! / [11! × 3 × 2 × 1]
¹⁴C₃ = (14 × 13 × 12) / (3 × 2 × 1)
¹⁴C₃ = 14 × 13 × 2
¹⁴C₃ = 364
The number of possible combinations of 14 objects taken 3 at a time will be 364.
Then the correct option is A.
More about the permutation and the combination link is given below.
https://brainly.com/question/11732255
#SPJ2
