\( 1<\begin{array}{l}\text { To win at LOTTO in one state, one must correctly select } 6 \text { numbers from a callection of } 68 \\ \text { numbers (1 through 56). The order in which the selection is made does not matter. Howt } \\ \text { many different selections are possible? }\end{array} \) There are \( \square \) different LOTTO selections.

It seems there was an error in the calculation. Let's simplify the expression manually: \[ C(68, 6) = \frac{68!}{6! \times 62!} \] Now, we can calculate the number of different selections possible in LOTTO. Simplify the expression by following steps: - step0: Solution: \(\frac{68!}{\left(6!\times 62!\right)}\) - step1: Remove the parentheses: \(\frac{68!}{6!\times 62!}\) - step2: Expand the expression: \(\frac{68\times 67\times 66\times 65\times 64\times 63\times 62!}{6!\times 62!}\) - step3: Reduce the fraction: \(\frac{68\times 67\times 66\times 65\times 64\times 63}{6!}\) - step4: Multiply the terms: \(\frac{78806407680}{6!}\) - step5: Calculate the value: \(\frac{78806407680}{720}\) - step6: Reduce the fraction: \(109453344\) The number of different selections possible in LOTTO is \( 1.094533 \times 10^8 \) or \( 109,453,344 \). Therefore, there are \( 109,453,344 \) different LOTTO selections.