Question

Pls help!! i rlly need this quick

Answer 1

See below ~

Explanation:

Combination Rule

• ⁿCₓ = n! / (n - x)! x!

#1) ²²C₂₀

• ²²C₂₀ = 22! / 2! 20!
• 22 x 21 x 20! / 2! x 20!
• 22 x 21 / 2
• 11 x 21
• 231

#2) ¹²C₈

• ¹²C₈ = 12! / 4! 8!
• 12 x 11 x 10 x 9 x 8! / 4! x 8!
• 12 x 11 x 10 x 9 / 4 x 3 x 2
• 11 x 5 x 9
• 99 x 5
• 495

Answer 2

`\displaystyle ^(22)C_(20) =231`

`\displaystyle ^(12)C_(8) =495`

Explanation:

Binomial Coefficients

`\displaystyle \binom{n}{r} \: = \:^(n)C_(r) = (n!)/((n-r)! \, r!)`

`\begin{aligned}\displaystyle \implies ^(22)C_(20) & = (22!)/((22-20)! \, 20!)\\\\ & =(22!)/(2! \, 20!)\\\\ & =(22 \cdot 21 \cdot 20!)/(2! \, 20!)\\\\ & =(22 \cdot 21)/(2 \cdot 1)\\\\ & =(462)/(2)\\\\ & =231\end{ailgned}`

`\displaystyle \begin{aligned} \implies ^(12)C_(8) & = (12!)/((12-8)! \, 8!)\\\\ & =(12!)/(4! \, 8!)\\\\ & =(12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!)/(4! \, 8!)\\\\ & =(12 \cdot 11 \cdot 10 \cdot 9)/(4 \cdot 3 \cdot 2 \cdot 1)\\\\ & =(11880)/(24)\\\\ & =495\end{aligned}`