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? O 720 O 1,440 20,358,520 o 312 18,009,460

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To determine the number of different selections possible, we use the combination formula since the order of selection does not matter. The number of ways to choose 6 numbers out of 52 is given by

$$
\binom{52}{6} = \frac{52!}{6!(52-6)!} = \frac{52!}{6! \times 46!}.
$$

We can simplify this expression by writing the numerator as the product of the 6 highest factors and canceling out the common factors in the denominator:

$$
\binom{52}{6} = \frac{52 \times 51 \times 50 \times 49 \times 48 \times 47}{6 \times 5 \times 4 \times 3 \times 2 \times 1}.
$$

Now, calculate the numerator step by step:

1. $$52 \times 51 = 2652$$.
2. $$2652 \times 50 = 132600$$.
3. $$132600 \times 49 = 6497400$$.
4. $$6497400 \times 48 = 311875200$$.
5. $$311875200 \times 47 = 14658134400$$.

Next, calculate the denominator:

$$
6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720.
$$

Now, divide the numerator by the denominator:

$$
\frac{14658134400}{720} = 20358520.
$$

Thus, the number of different selections possible is

$$
\boxed{20358520}.
$$
There are 20,358,520 different selections possible.

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? O 720 O 1,440 20,358,520 o 312 18,009,460

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