$$ \frac{{ }_{6} \mathrm{C}_{5}}{{ }_{9} \mathrm{C}_{5}}=\square $$ (Simplify your answer.)

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Let $$ {}_6C_5 $$ be the number of ways to choose 5 objects out of 6 and $$ {}_9C_5 $$ be the number of ways to choose 5 objects out of 9.

**Step 1: Evaluate $$ {}_6C_5 $$**

$$
{}_6C_5 = {}_6C_1 = 6
$$

**Step 2: Evaluate $$ {}_9C_5 $$**

$$
{}_9C_5 = \frac{9!}{5!(9-5)!} = \frac{9!}{5! \cdot 4!} = \frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1} = \frac{3024}{24} = 126
$$

**Step 3: Form the fraction and simplify**

$$
\frac{{}_6C_5}{{}_9C_5} = \frac{6}{126} = \frac{6 \div 6}{126 \div 6} = \frac{1}{21}
$$

The simplified answer is $$ \frac{1}{21} $$.
$$ \frac{1}{21} $$

(Simplify your answer.)

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