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17c517c5

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Full solution

Q. 17c517c5
  1. Identify Combination Formula: Identify the combination formula for 17c517c5. \newline17c5=17!5!(17−5)!17c5 = \frac{17!}{5!(17 - 5)!}
  2. Simplify Expression: Simplify the expression. 17c5=17!(5!×12!)17c5 = \frac{17!}{(5! \times 12!)}
  3. Expand Factorials: Expand the factorials where necessary.\newline17c5=17×16×15×14×13×12!5×4×3×2×1×12!17c5 = \frac{17 \times 16 \times 15 \times 14 \times 13 \times 12!}{5 \times 4 \times 3 \times 2 \times 1 \times 12!}
  4. Cancel Common Factorial: Cancel out the common 12!12! factorial.17c5=17×16×15×14×135×4×3×2×117c5 = \frac{17 \times 16 \times 15 \times 14 \times 13}{5 \times 4 \times 3 \times 2 \times 1}
  5. Perform Division and Multiplication: Perform the division and multiplication. 17c5=17×16×3×14×13117c5 = \frac{17 \times 16 \times 3 \times 14 \times 13}{1}

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