Question

The only way to learn counting is to practice, practice, practice, so here is your chance to do so. for this problem, you do not need to show work that justifies your answers. we encourage you to leave your answer as an expression (rather than trying to evaluate it to get a specific number). (a) how many ways are there to arrange n 1s and k 0s into a sequence? (b) a bridge hand is obtained by selecting 13 cards from a standard 52-card deck. the order of the cards in a bridge hand is irrelevant. how many different 13-card bridge hands are there? how many different 1

Answer 1

For a binary string of k zeros and n ones we choose n of them to be ones:

`\displaystyle {k + n \choose n} = ((k+n)!)/(k!n!)`

Bridge hands, we choose 13 of 52

`\displaystyle {52 \choose 13} = (52!)/(13!(52-13)!)`