There are k sets of numbers : {0,1,2,….,m1}, {0,1,2,……..,m2}, …………,{0,1,2,………,mk}
Such that m1<m2<………<mk.
1. How many combinations of k elements can be made taken 1 element from each set such that each set has all distinct elements (no two elements are equal) ?
2. What is the probability that any two sets will have at least one element common ?
(Please provide procedure and explanation)
I have found that the number of such permutations will be (m1+1)m2(m3-1)......(mk-k+2), but what will be the number of combinations ? Clearly it can not be just = No. of permutations / k!
N.B. - Please mention the formula/rules you've used so that I can learn them.
Such that m1<m2<………<mk.
1. How many combinations of k elements can be made taken 1 element from each set such that each set has all distinct elements (no two elements are equal) ?
2. What is the probability that any two sets will have at least one element common ?
(Please provide procedure and explanation)
I have found that the number of such permutations will be (m1+1)m2(m3-1)......(mk-k+2), but what will be the number of combinations ? Clearly it can not be just = No. of permutations / k!
N.B. - Please mention the formula/rules you've used so that I can learn them.