Question

if C (n,10) = C(n,12) then find the value of C(23,n)​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

$\sf{\large{ {}^{n} C_p} = \large{ {}^{n} C_q} \ \: implies \: n = p + q \: \: (provided \: p \ne \: q \: )}$

GIVEN

$\sf{\large{ {}^{n} C_{10}} = \large{ {}^{n} C_{12}} }$

TO DETERMINE

$\sf{\large{ {}^{23} C_{n}} }$

CALCULATION

By the above mentioned formula we get

$\sf{\large{ {}^{n} C_{10}} = \large{ {}^{n} C_{12}} }$

$\implies \: n = 10 + 12$

$\implies \: n = 22$

So

$\sf{\large{ {}^{23} C_{n}} }$

$= \sf{\large{ {}^{23} C_{22}} }$

$= 23$

Answer 2

Answer:

$\displaystyle\huge\red{\underline{\underline{Solution}}}Solution</p><p></p><p>FORMULA TO BE IMPLEMENTED</p><p></p><p>\sf{\large{ {}^{n} C_p} = \large{ {}^{n} C_q} \ \: implies \: n = p + q \: \: (provided \: p \ne \: q \: )}nCp=nCq impliesn=p+q(providedp≠q)</p><p></p><p>GIVEN</p><p></p><p>\sf{\large{ {}^{n} C_{10}} = \large{ {}^{n} C_{12}} }nC10=nC12</p><p></p><p>TO DETERMINE</p><p></p><p>\sf{\large{ {}^{23} C_{n}} }23Cn</p><p></p><p>CALCULATION</p><p></p><p>By the above mentioned formula we get</p><p></p><p>\sf{\large{ {}^{n} C_{10}} = \large{ {}^{n} C_{12}} }nC10=nC12</p><p></p><p>\implies \: n = 10 + 12⟹n=10+12</p><p></p><p>\implies \: n = 22⟹n=22</p><p></p><p>So</p><p></p><p>\sf{\large{ {}^{23} C_{n}} }23Cn</p><p></p><p>= \sf{\large{ {}^{23} C_{22}} }=23C22</p><p></p><p>= 23=23</p><p></p><p>$

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