Question

Calculate.
35 C12
Note: nCr=r(n=r)!
n!

Answer 1

$\\ \rm\Rrightarrow {}^{35}C_{12}$

$\\ \rm\Rrightarrow \dfrac{35!}{12!(35-12)!}$

$\\ \rm\Rrightarrow \dfrac{35!}{12!23!}$

$\\ \rm\Rrightarrow \dfrac{1.0333148e+40}{12383157381152686026522624000000}$

$\\ \rm\Rrightarrow 834451800$

Answer 2

Answer:

834,451,800

Step-by-step explanation:

Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Example:  4! = 4 × 3 × 2 × 1

Binomial Coefficient

$\large \text{ \rm ^{n}C_r=\dfrac{n!}{(n-r)!r!} }$

$\large \text{ \rm \implies ^{35}C_{12}=\dfrac{35!}{(35-12)!12!} }$

$\large \text{ \rm \implies ^{35}C_{12}=\dfrac{35!}23!12!} }$$\large \text{ \rm \implies ^{35}C_{12}=\dfrac{35!}{23!12!} }$

$\large \text{ \rm \implies ^{35}C_{12}=\dfrac{35 \times 34 \times 33 \times ... \times 25 \times 24}{12!} }$

$\large \text{ \rm \implies ^{35}C_{12}=834451800 }$