Binomial coefficients in practice

The following exercises are solved in this step.

We invite you to try to solve them before watching the video.

In any case, you will find below a PDF file with the solutions.

Exercise 1.

Count in how many ways one can choose 3 cards in a deck of 10 cards.

Exercise 2.

Prove that for (0leq kleq n) it is (displaystylebinom nk=binom n{n-k}).