In a bag there are w white balls and b black ball. In how many distinct ways one can choose k balls, without replacement, from this bag. Also, In how many distinct ways one can choose k balls, such that ith ball is white.
Choosing from a collection of 2 classes of identical objects.
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$\begingroup$
probability
combinatorics
combinations
1 Answers
3
We can use binomial coefficients.
There are ${ {w + b} \choose k}$ way to choose balls without replacement.
The ith ball being white is by symmetry the same as the first ball being white. So ${ {w + b - 1} \choose {k-1}}$ ways.