How many different ways are there to select three days of the week?

`7 xx 6 xx 5`

`(7 xx 6 xx 5) / 3`

`(7 xx 6 xx 5) / (1 xx 2 xx 3)`

`(7 xx 6 xx 5 xx 4 xx 3) / (1 xx 2 xx 3 xx 4 xx 5)`

Which of these can be calculated as `(20 xx 19 xx 18 xx 17) / (1 xx 2 xx 3 xx 4)`?

`((16),(4))`

`((17),(4))`

`((24),(4))`

`((20),(16))`

If a judge must select three winners from 10 contestants, which of the following is NOT true?

If they simply choose three overall winners, there are `((10),(3))` possible outcomes.

If they specifically identify who gets first place, who gets second place, and who gets third place, there are `((10),(1))((9),(1))((8),(1))` possible outcomes.

There are exactly 10 + 9 + 8 ＝ 27 more possible outcomes if they choose first, second, and third place individually instead of choosing three overall winners.

There are exactly 3 × 2 × 1 ＝ 6 times as many possible outcomes if they choose first, second, and third place individually instead of choosing three overall winners.

Analisa deals one card to Troy, two cards to Steve, and three cards to Owen. How many possibilities are there for who gets which card?

`((52),(6))`

`((52),(1))((51),(2))((49),(3))`

`((52),(1))((52),(2))((52),(3))`

`((52),(1))((51),(1))((50),(1))((49),(1))((48),(1))((47),(1))`