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

Answer:

The probability of picking exactly 4 of the 6 numbers​ correctly is $\frac{15}{5245786}=2.859 \times 10^{-6}$

Step-by-step explanation:

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

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

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

$C^{6}_{4}=\frac{6!}{(6-4)! \ 4!}=\frac{6 *5*4*3*2*1}{(2*1) \times (4*3*2*1)}=\frac{30}{2}=15$

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)= $\frac{15}{5245786}$