Question

a) you can pick 6 different numbers for a betting ticket. How many selections are possible?b) if prizes will be paid to those picking 4 to 6 drawn numbers, how many winning selections are possible?

Answer 1

`\begin{gathered} a)\text{ 13,983,816} \\ b)\text{ 15,180} \end{gathered}`

Step-by-step explanation:

a) Here, we want to get the number of possible selections

Mathematically, that would be selecting 6 out of 49

We can calculate this using combination as follows

We have that as:

`^(49)C_6\text{= }(49!)/((49-6)!6!)\text{ = 13,983,816}`

b) What this means is that, winnings would only be paid to tickets with 4,5,6 in them while the other 3 numbers can be anything

What this means is that we would be selecting 3 out of 46 numbers

Mathematically, we use the combination rule again as follows:

`^(46)C_3\text{ = }(46!)/((46-3)!3!)\text{ = 15,180}`