The number of ways to pick 6 different numbers from 1 to 42 in a state lottery is 5,245,786. assuming order is unimportant, what is the probability of picking exactly 4 of the 6 numbers correctly?

The probability of picking exactly 4 of the 6 numbers correctly is

Step-by-step explanation:

As order is unimportant, we have to calculate the different outcomes with combinations formula:

The total outcomes of picking exactly 4 of the 6 numbers is:

The probability of picking exactly 4 of the 6 numbers correctly is given by:

Total outcomes by picking 6 numbers from 1 to 42: 5245786

P(4 of the 6 numbers are correct)=

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)