Final answer:
To determine how many ways three Systems Engineer positions can be filled from 20 applicants, we calculate 20P3, which gives us 6,840 different permutations, making option B correct.
Step-by-step explanation:
The question asks how many different ways can three Systems Engineer positions be filled from a pool of 20 applicants. To solve this, we need to use permutations since the order in which the positions are filled matters. In permutation, positions are distinct, so we will calculate this as 20P3 (20 permutation 3), which means picking 3 out of 20 with order being significant.
The formula for permutations is nPr = n! / (n-r)!, where n is the total number and r is the number selected. In this case, 20P3 = 20! / (20-3)! = 20! / 17! = 20 × 19 × 18. Calculating this gives 6,840 different ways the positions could be filled. Therefore, option B) "21 Permutation; 6,840" is the correct answer.