Final answer:
To calculate the number of ways to pick exactly 6 out of 7 winning numbers from a range of 1 to 72, use combinatorial calculations. There are 455 ways to achieve this, determined by multiplying the number of ways to choose 6 winning numbers (7) by the number of ways to choose 1 non-winning number (65).
Step-by-step explanation:
To calculate the number of ways you can pick exactly 6 of the 7 winning numbers in a lottery game, where you choose 7 different numbers from 1 to 72, we can use the concept of combinations.
The problem involves choosing 6 winning numbers from the 7 drawn and 1 non-winning number from the remaining 65 numbers (72 - 7).
First, we calculate the combination of choosing 6 numbers from the 7 winning numbers. This can be done in C(7, 6) ways, which equals 7.
Next, we need to choose 1 non-winning number from the 65 non-winning numbers, which can be done in C(65, 1) ways, which equals 65.
Since these actions are independent, we can multiply the two combinations to find the total number of ways to pick exactly 6 winning numbers: 7 × 65 = 455 ways.