Question

To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 52 numbers (1 through 52.) The order in which the selections is made does not matter. How many different selections are possible

Answer 1

Answer:  14,658,134,400

Step-by-step explanation:

There are 52 numbers to start with.  After choosing the first number, there are 51 numbers remaining, etc.

1st   and   2nd   and   3rd    and   4th  and   5th  and  6th

52    x       51       x      50      x       49    x      48     x     47  = 14,658,134,400

You can also find the answer using the following formula:

$\dfrac{52!}{(52-6)!}=\dfrac{52!}{46!}=\dfrac{52\times 51\times 50\times 49\times 48\times 47 \times 46!}{46!}\\\\\\.\qquad \qquad \qquad \quad = 52\times 51\times 50\times 49\times 48\times 47\\ \\\\.\qquad \qquad \qquad \quad =\large\boxed{14,658,134,400}$