If nC10 = nC12, Find 23Cn. - Vidyadip

Question

If ⁿC₁₀ = ⁿC₁₂, Find ²³C_n.

✓

Answer

We have,
If ⁿC_p = ⁿC_q = n
Then p + q = n
Also,
⇒ ⁿC₁₀ = ⁿC₁₂
10 + 12 = n
⇒ n = 22
Applying (i),
${^\text{23}}\text{C}_{\text{22}}=\frac{\text{23!}}{22!1!}$
$=\frac{23\times22!}{22!}$
$=23$

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