Combinations Property for nC3 = nC8
We are given the equation $^nC_3 = ^nC_8$.
Recall the property of combinations: $^nC_r = ^nC_k$ holds true if either:
- $r = k$
- $n = r + k$
In this problem, we have $r=3$ and $k=8$. Since $3 \neq 8$, we must use the second condition.
Finding the value of n
- Apply the condition $n = r + k$.
- Substitute the given values: $n = 3 + 8$.
- Calculate the sum: $n = 11$.
Therefore, the value of n is 11.
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