the expression $_{n}c_{r}$ represents the number of combinations when $r$ items are selected from $n$ items.

use the combination formula shown below to find $_{47}c_{8}$.

\_{n}c_{r} = \frac{n!}{(n-r)!r!}\

substitute for $n$ and $r$ and simplify the expression.

\_{n}c_{r} = \frac{n!}{(n-r)!r!}\

\_{47}c_{8} = \frac{47!}{(8 - 39)!8!}\

Question

the expression $_{n}c_{r}$ represents the number of combinations when $r$ items are selected from $n$ items.

use the combination formula shown below to find $_{47}c_{8}$.

\_{n}c_{r} = \frac{n!}{(n-r)!r!}\

substitute for $n$ and $r$ and simplify the expression.

\_{n}c_{r} = \frac{n!}{(n-r)!r!}\

\_{47}c_{8} = \frac{47!}{(8 - 39)!8!}\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Combinations Formula" ], "new_concepts": [], "current_concepts": [ "Combinations Formula" ] } ## Identify the values of n and r $$ \begin{aligned} &n = 47 \ &r = 8 \end{aligned} $$ ## Substitute into the combination formula $$ \begin{aligned} &_nC_r = \frac{n!}{(n-r)!r!} \ &_{47}C_8 = \frac{47!}{(47-8)!8!} \end{aligned} $$ ## Simplify the denominator term $$ 47 - 8 = 39 $$ Substitute for n and r and simplify the expression. $$ \begin{aligned} _nC_r &= \frac{n!}{(n-r)!r!} \ _{47}C_8 &= \frac{\boxed{47}!}{(\boxed{47}-\boxed{8})!\boxed{8}!} \end{aligned} $$ The filled expression is: $_{47}C_8 =$ $\frac{47!}{(47-8)!8!}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Combinations Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the values of n and r

Substitute into the combination formula

Simplify the denominator term

Answer: