Permutations and Combinations flashcards

Question 1

What is the factorial $n!$ for a nonnegative integer $n$?

Accepted Answer

$$n! = n(n-1)(n-2)\cdots\cdot 2\cdot 1	ext{ for }n\ge 1,\qquad 0!=1.$$

Question 2

State the formula for combinations of $r$ objects chosen from $n$ distinct objects (no repetition).

Accepted Answer

$$C(n,r)=\binom{n}{r}=\frac{n!}{r!(n-r)!},\quad 0\le r\le n.$$ Here $n$ is total items and $r$ is number selected (order ignored).

Question 3

What is a binomial coefficient, and where does it appear?

Accepted Answer

The binomial coefficient is $\binom{n}{r}$, the number of ways to choose $r$ items from $n$. It appears in the binomial theorem: $$(a+b)^n=\sum_{r=0}^{n}\binom{n}{r}a^{n-r}b^r.$$

Permutations and Combinations flashcards

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