Answer: The number of different ways the teacher can choose the team of three students from a class of 23, where the order of the speakers is not important, is 1771.
Explanation:
To solve this problem, we can use the combination formula:
nCr = n! / r!(n - r)!
where n is the total number of items, r is the number of items to be selected, and ! represents factorial, which means the product of all positive integers up to the given number.
In this case, we need to choose 3 students out of 23, without regard to the order in which they will speak. Therefore, we need to use the combination formula with n = 23 and r = 3:
23C3 = 23! / (3!(23 - 3)!)
= 23! / (3!20!)
= (23 × 22 × 21) / (3 × 2 × 1)
= 1771
Therefore, there are 1771 different ways the teacher can choose the team of three students for the competition, where the order of the speakers is not important.