Answer to Question #8173 in Statistics and Probability for BAM MacDaniels

Question

If I have 5 ten sided dice, what is the probability that all of them will show numbers 1-7? What about only 4? What about only 3, or 2, or 1, or none?

Answer 1

For 5 ten sided dice the probability that all of them will show numbers 1-7 is
(7/10)^5=16.81%
For 5 ten sided dice the probability that only 4 of them will
show numbers 1-7 is (3/10)* (7/10)^4=7.20%
For 5 ten sided dice the
probability that only 3 of them will show numbers 1-7
is((3/10)^2)*(7/10)^3=3.01%
For 5 ten sided dice the probability that only 2
of them will show numbers 1-7 is ((3/10)^3)*(7/10)^2=1.32%
For 5 ten sided
dice the probability that only 1 of them will show numbers 1-7 is
(7/10)*(3/10)^4=0.57%
For 5 ten sided dice the probability that none of them
will show numbers 1-7 is (3/10)^5=0.24%