Question

A word game has 100 tiles with different letters. If letters are drawn 7 at a time, approximately how many possible letter combinations exist

Answer 1

from my understanding, since all the letters go into the same hand, it doesn't matter how the letters are arranged within the hand (ex: abcdefg gets treated the same as acbdgef, etc.).

therefore, we should use the combination formula.

combnination formula for choosing (r) items from (n) possibilities:

nCr = \[\frac{ n! }{ r!(n-r)! }\]

in this case, your n value is 100 since there are 100 tiles, and r = 7 since there are 7 tiles being chosen at a time. plug in and evaluate.