Question

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?

Answer 1

The probability of picking exactly 4 of the 6 numbers​ correctly is
`(15)/(5245786)=2.859 * 10^(-6)`

Explanation:

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

`C^(n)_(r)=(n!)/((n-r)! \ r!)`

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

`C^(6)_(4)=(6!)/((6-4)! \ 4!)=(6 *5*4*3*2*1)/((2*1) * (4*3*2*1))=(30)/(2)=15`

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)=
`(15)/(5245786)`