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Permutations , combinations and binomial expansion — Statistics STD 11 Commerce — Question

Gujarat BoardEnglish MediumSTD 11 CommerceStatisticsPermutations , combinations and binomial expansion1 Mark
Question
Obtain the values of : ${ }^{25} C_{23}$
✓

Answer

$
\begin{aligned}
& { }^n C_r=\frac{n !}{r !(n-r) !} \\
& \therefore{ }^{25} C_{23}=\frac{25 !}{23 !(25-23) !} \\
& =\frac{25 !}{23 ! 2 !} \\
& =\frac{25 \times 24 \times 23 !}{23 ! \times 2 \times 1}=\frac{600}{2}=300
\end{aligned}
$

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