Write a Java program that has the following inputs and outputs: Given a positive integer n and a nonnegative integer r not exceeding n:

1.Find the number of r-permutations and r-combinations of a set with n elements.

* r-permutations

If n is a positive integer and r is an integer with 1 r n,

then there are

Note that P(n,0) = 1, since there is only one way to order zero elements.

Example

P(100,3) = 970,200

* r-combinations

n r 0

Example

r = 52 - 5 = 47 or r = 5

2.Find the probability of selecting the six integers from the set {1, 2, . . . , n} that were mechanically selected in a lottery.

Example

40 - 6= 34