How many experimental runs exist in a Full Factorial and fully randomized design for 5 factors with 2 replicates for the Corner Points and no Center…

A full factorial design with 5 factors at 2 levels consists of $2^5 = 32$ corner points (experimental runs). Since the design includes 2 replicates for each corner point and no center points, the total number of experimental runs is calculated by multiplying the number of corner points by the number of replicates. Therefore, $32 \times 2 = 64$ total experimental runs.

A. 10 is incorrect because it does not correspond to any standard $2^k$ factorial design calculation for 5 factors.

B. 128 is incorrect; this would be the number of runs for a 7-factor full factorial design ($2^7$) or a 5-factor design with 4 replicates.

C. 256 is incorrect; this represents an 8-factor full factorial design ($2^8$) without replicates.

- Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). John Wiley & Sons. Section 6.2, p. 234.

- NIST/SEMATECH e-Handbook of Statistical Methods, Section 5.3.3.3. "Full Factorial Designs".