SOLUTION: If a child is given cards with A, C, D, G, O, and T on them, what is the probability he or she could spell GOT by guessing the correct arrangement of 3 cards from the 6?

Algebra ->  Probability-and-statistics -> SOLUTION: If a child is given cards with A, C, D, G, O, and T on them, what is the probability he or she could spell GOT by guessing the correct arrangement of 3 cards from the 6?      Log On


   

Question 867517: If a child is given cards with A, C, D, G, O, and T on them, what is the probability he or she could spell GOT by guessing the correct arrangement of 3 cards from the 6?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the probability will be 1 / 6P3 which is equal to 1/120.

there are 6P3 possible number of ordered arrangement of sets of 3 cards taken from 6.

6P3 is the formula for the permutation of 6 things taken 3 at a time.

that equals 6! / 3! which is equal to 6*5*4 which is equal to 120.

a permutation is an ordered arrangement.

the general formula for a permutation of n things taken x at a time is:

nPx = n! / (n-x)!

when n = 6 and x = 3, this becomes 6P3 = 6! / (6-3)! which becomes 6! / 3!.