Question

Which of the following is equal to C(10, 3)?
C(3, 10)
C(10, 7)
P(10, 3)

Answer 1

P

Explanation:

C and P are both (10,3).

Answer 2

Presumably C(10,3) refers to the combinations of 10 things taken three at a time, often written

`\displaystyle {10 \choose 3}`

When we choose three of 10, we're actually also choosing seven of 10, the leftovers. So there are the same number of combinations of three as combinations of seven. In general

`\displaystyle {n \choose k}={n \choose n-k}`

Answer: C(10,7)