Question

A bag contains 10 tiles with the letters A, B, C, D, E, F, G, H, I, and J. Five tiles are chosen, one at a time, and placed in a row. Meghan says that the probability of the five tiles spelling FACED is 1/252 . Her work is shown below.

Answer 1

I assume in this item, we are to find at which step is the mistake done for the calculation of the unknown probability.

For the possible number of arrangement of letter, n(S), the basic principles of counting should be used.
= 10 x 9 x 8 x 7 x 6 = 30,240

This is similar as to what was done in Meghan's work.

For the five tiles to spell out FACED, there is only one (1) possibility.

Therefore, the probability should be equal to 1/30,240 instead of the 1/252 which was presented in the steps above.