QuestionJuly 16, 2025

Evaluate the expression. (C(8,6)cdot C(9,7))/(C(13,9)) square

Evaluate the expression. (C(8,6)cdot C(9,7))/(C(13,9)) square
Evaluate the expression.
(C(8,6)cdot C(9,7))/(C(13,9))
square

Solution
4.0(272 votes)

Answer

\frac{72}{55} Explanation 1. Calculate C(8,6) Use the formula for combinations: **C(n,k) = \frac{n!}{k!(n-k)!}**. So, C(8,6) = \frac{8!}{6!2!} = \frac{8 \times 7}{2 \times 1} = 28. 2. Calculate C(9,7) Similarly, C(9,7) = \frac{9!}{7!2!} = \frac{9 \times 8}{2 \times 1} = 36. 3. Calculate C(13,9) C(13,9) = \frac{13!}{9!4!} = \frac{13 \times 12 \times 11 \times 10}{4 \times 3 \times 2 \times 1} = 715. 4. Evaluate the Expression Substitute the values: \frac{C(8,6) \cdot C(9,7)}{C(13,9)} = \frac{28 \cdot 36}{715}. 5. Simplify the Fraction Calculate: \frac{1008}{715}. Simplifying gives \frac{72}{55}.

Explanation

1. Calculate $C(8,6)$<br /> Use the formula for combinations: **$C(n,k) = \frac{n!}{k!(n-k)!}$**. So, $C(8,6) = \frac{8!}{6!2!} = \frac{8 \times 7}{2 \times 1} = 28$.<br /><br />2. Calculate $C(9,7)$<br /> Similarly, $C(9,7) = \frac{9!}{7!2!} = \frac{9 \times 8}{2 \times 1} = 36$.<br /><br />3. Calculate $C(13,9)$<br /> $C(13,9) = \frac{13!}{9!4!} = \frac{13 \times 12 \times 11 \times 10}{4 \times 3 \times 2 \times 1} = 715$.<br /><br />4. Evaluate the Expression<br /> Substitute the values: $\frac{C(8,6) \cdot C(9,7)}{C(13,9)} = \frac{28 \cdot 36}{715}$.<br /><br />5. Simplify the Fraction<br /> Calculate: $\frac{1008}{715}$. Simplifying gives $\frac{72}{55}$.
Click to rate:

Similar Questions