## anonymous one year ago Fan and Medal!... A lottery is set up in which players pick six numbers from the set 1, 2, 3, ... , 39, 40. How many different ways are there to play this lottery? (In this game the order in which the numbers are picked does NOT matter.)

1. anonymous

@kropot72

2. kropot72

This problem asks for the number of combinations of 40 numbers taken 6 at a time. There are 40 choices for the first number, having chosen the first number there are 39 choices for the second number, 38 choices for the third number, and so on giving $40\times39\times38\times37\times36\times35=(you\ can\ calculate)\ ways$

3. anonymous

276,363,3600?

4. kropot72

However the question states that order of selection does not matter, therefore the result of the above calculation must be divided by $\large 6\times5\times4\times3\times2\times1$ this being the number of permutations of each selection.

5. anonymous

720

6. kropot72

So we have $\large \frac{2,763,633,600}{6\times5\times4\times3\times2\times1}$

7. kropot72

Yes, the denominator is 720.

8. anonymous

thank you so much @kropot72 sorry for the late responses im on babysitting duty

9. kropot72

You're welcome :)