In a football team (11 people), a captain and his deputy need to be selected. How many ways can this be done

#
The captain can be any of the 11 football players. After choosing the captain, the role of his deputy can be claimed by any of the 10 remaining players. Thus, there are $11 \cdot 10=110$ different variants.

## Answer

110 ways.

At the dance floor, $N$ young men and $N$ young women have gathered. In how many ways can they pair up to participate in the next dance?

## Hint

"Fix" the women. Then, the pairing is determined by the permutation of the men.

## Answer

$N$! ways.