To win at LOTTO in one state, one must correctly select 6 numbers from a collection of 56 numbers (1 through 56 ). The order in which the selection is made does not matter. How many different selections are possible? There are \( \square \) different LOTTO selections.

To determine the number of different selections of 6 numbers from a set of 56, you can use the combination formula: \[ C(n, r) = \frac{n!}{r!(n - r)!} \] In this case, \( n = 56 \) and \( r = 6 \): \[ C(56, 6) = \frac{56!}{6!(56 - 6)!} = \frac{56!}{6! \times 50!} \] Calculating this gives: \[ C(56, 6) = \frac{56 \times 55 \times 54 \times 53 \times 52 \times 51}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \] After simplifying, you find there are 3,838,380 different LOTTO selections. So, there are \( 3,838,380 \) different LOTTO selections. Did you know that the concept of combinations dates back to ancient Chinese and Indian math? The earliest known use of combinations was in a 2nd-century Chinese text while mathematicians like Brahmagupta in India also explored them! These smart cookies laid the groundwork for the combinatorial principles we still use in games like LOTTO today! Now, if you're thinking of trying your luck in the LOTTO, remember that while picking numbers might seem like a fun and whimsical game, most players choose numbers based on special dates. This can limit your range to numbers 1 through 31! Instead, consider a wider spread for better coverage and less chance of sharing a jackpot. Just a little strategy to maximize that million-dollar dream!