If $^nC_4={}^nC_6$, find $^{12}C_n$.

If ⁿC₄=ⁿC₆, find ¹²Cₙ.

Question 40 of 48

^nC_4={}^nC_6

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Solving $^nC_4={}^nC_6$ gives $n=10$ , so $^{12}C_n={}^{12}C_{10}=66$ .

Step 1 — find $n$ . Use the property: if $^nC_a={}^nC_b$ (with $a\neq b$ ), then $a+b=n$ . Here $a=4,\ b=6$ :

$n=4+6=10.$

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