Problem Solving

Each participant in a certain study was assigned a sequence of 3 different letters form 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? (Note, A,B,C is different from C,B,A.)

20
92
300
372
476

I got the correct answer, just putting it out there for different approaches. Enjoy.

Lemme have a crack at it.

Since order matters, it must be permutation.

Now, 3 letters can be selected from 8 in 8P3 ways = 336 ways.

Since 36 possible sequences are not assigned to any participant,

Number of distinct participants = 336-36 = 300.

Hope this is correct!

Answer C!

Birottam Dutta wrote:Lemme have a crack at it.

Since order matters, it must be permutation.

Now, 3 letters can be selected from 8 in 8P3 ways = 336 ways.

Since 36 possible sequences are not assigned to any participant,

Number of distinct participants = 336-36 = 300.

Hope this is correct!

Answer C!

You got it

8p3-36 = 336-36 = 300