What is the minimum number of bits required (optimal encoding) to encode each powerball lottery ticket? (please show all your work.)

Let's say you buy one ticket for the California Powerball lottery. This means that you can make a powerball selection. A powerball selection is composed of two parts: a subset of 5 integers from the set {1,2,3,...,69}; and 1 (powerball) integer from the set {1,2,3,..., 26} (the powerball integer could be the same as or different than any of the original 5 integers.) Examples of winning powerball selections this year so far: Date set of 5 Powerball Jan 23, 2021 (5,8, 17, 27, 28} 14 Jan 20, 2021 {40, 53, 60, 68, 69} 22 Jan 16, 2021 {14, 20, 39, 65, 67} 2 Jan 13, 2021 | {4, 19, 23, 25, 49} 14 Jan 9, 2021 {14, 26, 38, 45, 46) 13 Jan 6, 2021 {1,20, 22,60,66} Jan 2, 2021 {3, 4, 11, 41, 67} 5 3