Answer:
[tex]^{24}\textrm{C}_{12}[/tex]
Step-by-step explanation:
Here we are given an expression which represents
[tex] ^{n}\textrm{C}_{r}[/tex]
This is a formula for problems related to combination from topic " Permutation and Combination"
The formula is
[tex]^{n}\textrm{C}_{r}=\frac{n!}{(n-r!)r!}[/tex]
Hence
[tex]^{24}\textrm{C}_{12}=\frac{24!}{(24-12)!12!}[/tex]
[tex]^{24}\textrm{C}_{12}=\frac{24!}{12!12!}[/tex]
[tex]^{24}\textrm{C}_{12}= \frac{24\times 23 \times 22 \times ...... 3 \times 2 \times 1}{(12\times 11\times 10\times ...... 3 \times 2 \times 1 ) \times (12\times 11\times 10\times ...... 3 \times 2 \times 1 )}[/tex]
[tex]^{24}\textrm{C}_{12}=\frac{24\times 23 \times 22 \times ...... 15\times 14 \times 13}{12\times 11\times 10\times ...... 3 \times 2 \times 1 }[/tex]
Solving above multiplication and division we get
[tex]^{24}\textrm{C}_{12}=2704156[/tex]
