Suppose I draw 5 numbers uniformly at random from 1 to 70, and suppose I do so twice. What is the probability that the smallest two numbers match, and no others?
So let a1<a2<a3<a4<a5 be the number from one draw, and let b1<b2<b3<b4<b5 be the number from the other draw. What is the probability that a1=b1, a2=b2, and a3, a4, a5, b3, b4, b5 are all different.
Is that your question?
How accurately do you need to know the answer? You can get an approximation quite quickly by simulation ... an exact answer will be horrible.
Edit: OK, I have answers, but it would be useful to know how accurately you need your answer.
Suppose I draw 5 numbers uniformly at random from 1 to 70, and suppose I do so twice. What is the probability that the smallest two numbers match, and no others?
So let a1<a2<a3<a4<a5 be the number from one draw, and let b1<b2<b3<b4<b5 be the number from the other draw. What is the probability that a1=b1, a2=b2, and a3, a4, a5, b3, b4, b5 are all different.
Is that your question?
How accurately do you need to know the answer? You can get an approximation quite quickly by simulation ... an exact answer will be horrible.
Edit: OK, I have answers, but it would be useful to know how accurately you need your answer.