In a state lottery, four digits are drawn at random one at a time with replacement from 0 to 9. Suppose that you win if any permutation of your selected integers is drawn. Give the probability of winning if you select

a) Probability (6,7,8,9) = 0.0024

b) Probability (6,7,8,8) = 0.0012

c) Probability (7,7,8,8) = 0.0006

d) Probability (7,8,8,8) = 0.0004

Step-by-step explanation:Permutation is given by the equation = n! / (n-r) !

P=4! / (4-4) !=4*3*2*1=24

Each digit has 10 possible ways

Total number of ways=10*10*10*10=10,000

a) Probability (6,7 8,9) = 24/10,000=0.0024

b) 6,7,8,8. 6 and 7 occured once but 8 occured twice

Using multinominal coefficient = 4! / (1!2!) = 24/2=12

Possible ways for6,7,8,8 = 10,000

Probability (6,7,8,8) = 12/10,000 = 0.0012

c) 7,7 8,8. 7 and 8 occured twice. Usining multinominal Coefficient=4! / (2!2!) = 24/4=6

Possible ways for 7,7,8,8=10,000

Probability (7,7,8,8) = 6/10,000=0.0006

d) 7,8,8,8,. 7 occured once while 8 occured three times. Using multinominal coefficient = 4! / (1!3!) = 24/6=4

Possible ways for7,8,8,8 = 10,000

Probability (7,8,8,8) = 4/10000=0.0004