Question

Each participant in a certain study was assigned a sequence of 3 different letters from the set {A, B, C, D, E, F, G, H}. If no sequence was assigned to more than one participant and if 36 of the possible sequences were not assigned, what was the number of participants in the study?

Answer 1

Number of possible sequence of 3 in 8 = 8P3 = 8! / (8-3)! = 336

36 were not assigned so number participants = 300 (answer).

Explanation:

Answer 2

300

Explanation:

We are given that

Total number of letters used =8

Letters used in one sequence=3

Each participant was assigned a sequence of 3 different letters.

Repetition is not allowed.

Total number of possible participants in the study=
`8P_3=(8!)/((8-3)!)=(8\cdot7\cdot6\cdot 5!)/(5!)=336`

But , we are given that number of possible sequence were not assigned=36

Therefore, total number of participants in the study=336-36=300