Imagine you have 21 boxes, each numbered 1 to 21. To choose 6 numbers with order mattering, it's like filling these boxes one by one. For the first box, you have 21 choices. For the second box, only 20 numbers remain. So far, there are 21 x 20 = 420 possibilities. You continue similarly for the remaining boxes, multiplying the available choices at each step: 420 x 19 x 18 x 17 x 16 x 15 = 39,070,080. Therefore, option (b) is the correct answer .
In this lottery, you're not just picking 6 numbers, you're building a specific sequence of 6. Think of it like making a 6-digit code on a numbered lock. For the first digit, you have 21 options (all the numbers!). So far, there are 21 potential codes.
But for the second digit, only 20 options remain (one number is already used). That means there are 21 ways to choose the first digit AND 20 ways to choose the second, making 21 x 20 = 420 possible codes after two picks.
The same logic applies for every subsequent digit. You keep multiplying the remaining options: 420 x 19 x 18 x 17 x 16 x 15 = a whopping 39,070,080 possible sequences! This is why order matters – each arrangement of the 6 numbers is a unique code, leading to this massive number of possibilities hence , option (b) is the correct answer .
So, if you're aiming to win this lottery by brute force (not recommended!), you'd need to try almost 39 million different combinations. Good luck!