Barker Griffiths
03/13/2024 · Senior High School
d) \( \binom{17}{14} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( \binom{17}{14} \).
Calculate the value by following steps:
- step0: Calculate:
\( { }_{17}C_{14}\)
- step1: Expand the expression:
\(\frac{17!}{14!\times \left(17-14\right)!}\)
- step2: Subtract the numbers:
\(\frac{17!}{14!\times 3!}\)
- step3: Expand the expression:
\(\frac{17\times 16\times 15\times 14!}{14!\times 3!}\)
- step4: Simplify:
\(\frac{17\times 16\times 15}{3!}\)
- step5: Multiply the terms:
\(\frac{4080}{3!}\)
- step6: Calculate the value:
\(\frac{4080}{6}\)
- step7: Reduce the fraction:
\(680\)
La expresión \( \binom{17}{14} \) es igual a 680.
Quick Answer
\( \binom{17}{14} = 680 \).
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