Answer:
The probability of picking exactly 4 of the 6 numbers correctly is [tex]\frac{15}{5245786}=2.859 \times 10^{-6}[/tex]
Step-by-step explanation:
As order is unimportant, we have to calculate the different outcomes with combinations formula:
[tex]C^{n}_{r}=\frac{n!}{(n-r)! \ r!}[/tex]
The total outcomes of picking exactly 4 of the 6 numbers is:
[tex]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[/tex]
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)= [tex]\frac{15}{5245786}[/tex]
