Question

To win at lotto in a certain state, one must correctly select 6 numbers from a collection of 50 numbers (one through 50). the order in which the selections is made does not matter. how many different selections are possible?

Answer 1

We have been given that the order doesn't matter in the selection procedure. Hence, the case is of combination.

The formula for the combination is given by

$^nC_r=\frac{n!}{r!(n-r)!}$

Now, in order to win at lotto, one must correctly select 6 numbers from a collection of 50 numbers. Thus, the required ways should be

$^{50}C_6$

Using the above formula, the number of different selections are

$^{50}C_6=\frac{50!}{6!(50-6)!}\\ \\ =\frac{50!}{6!44!}\\ \\ =\frac{44!\times 45\times 46\times 47 \times 48\times 49\times 50}{6!44!}\\ \\ =15890700$

Therefore, 15890700 different selections are possible.

Answer 2

Asked and answered elsewhere.
brainly.com/question/10013755