Math Problem Statement

Calculate the value of the mathematical expression (12 C5) · (7 C3).

Solution

The mathematical expression given in the image is:

(125)(73)\binom{12}{5} \cdot \binom{7}{3}

Solution:

  1. Calculate (125)\binom{12}{5}: (125)=12!5!(125)!=1211109854321=792\binom{12}{5} = \frac{12!}{5!(12-5)!} = \frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 792

  2. Calculate (73)\binom{7}{3}: (73)=7!3!(73)!=765321=35\binom{7}{3} = \frac{7!}{3!(7-3)!} = \frac{7 \cdot 6 \cdot 5}{3 \cdot 2 \cdot 1} = 35

  3. Multiply the results: (125)(73)=79235=27,720\binom{12}{5} \cdot \binom{7}{3} = 792 \cdot 35 = 27,720

Final Answer:

27,72027,720

Would you like additional details or explanation on combinations? Let me know!

Relative Questions:

  1. What are the general properties of binomial coefficients?
  2. How can we interpret combinations in probability and counting?
  3. How does the factorial function simplify expressions involving combinations?
  4. What is the difference between combinations and permutations?
  5. How can we calculate combinations efficiently for large numbers?

Tip:

When solving combinations, cancel out as many terms

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Binomial Coefficients
Factorials

Formulas

nCr = n! / [r! · (n - r)!]
(nCr) · (mCr)

Theorems

Binomial Coefficient Formula

Suitable Grade Level

Grades 9-12