Combinations Rule Your Life

Every password you type, every lottery ticket sold, and every genetic trait you inherited depends on combinatorial math. A 4-digit PIN has 10,000 possibilities; a 12-character password has hundreds of sextillions. The same counting tool sets your odds at the card table and your security online — small choices, astronomically large numbers.

Combinations explain selections where order does not matter, while other counting problems use related tools. DNA codons, for example, are ordered three-letter sequences over four bases, giving 4 x 4 x 4 = 64 possible codons. Biology, cryptography, and logistics all use combinatorics, but the first question is always the same: does order matter?