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

Answer: 16 007 560 800 possible letter combinations.
Explanation: Now, we don't care about the order in which they are picked, so it's a little bit different to how permutation probability and combinations work.
Since we don't care about order, these two are identical:

123a
12a3

They have the same letters in their sequence, so they won't form a new word.
Now, let's understand how combinatorics work compared to permutations.

Combinatorics work out a list of combinations that you can have, provided that they all have different values (123 is not the same as 234, they are different combinations), however permutations focus solely on ordered figures (123 may be the same as 321 in combinatorics, but they yield a new set in permutations).

Thus, if we don't care about order, let's write up a formula:
If we have 100 tiles to fill 100 places, we have 100! combinations, provided that they are all different letters.
But we only want to pick 7 and sort them out.

Thus, our equation is $\frac{100!}{7!(100 - 7)!} = 16 007 560 800$
This is our $^{n}C_r$ formula, and it's important to remember this formula.