Question

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

Answer 1

`\\ \rm\Rrightarrow {}^(35)C_(12)`

`\\ \rm\Rrightarrow (35!)/(12!(35-12)!)`

`\\ \rm\Rrightarrow (35!)/(12!23!)`

`\\ \rm\Rrightarrow (1.0333148e+40)/(12383157381152686026522624000000)`

`\\ \rm\Rrightarrow 834451800`

Answer 2

834,451,800

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=(n!)/((n-r)!r!) $}`

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

`\large \text{$ \rm \implies ^(35)C_(12)=\frac{35!}23!12!} $}`
`\large \text{$ \rm \implies ^(35)C_(12)=(35!)/(23!12!) $}`

`\large \text{$ \rm \implies ^(35)C_(12)=(35 * 34 * 33 * ... * 25 * 24)/(12!) $}`

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