Question

If 100C3 = 161700 then 100C97 is equal to ..............(Permutation Combination)

Answer 1

Given,

100C3 = 161700

To Find,

100C97 = ?

Solution,

100C3

==> (100!)/3!(100 - 3)!

==> (100!)/3! * 97!

==> (100 * 99 * 98 * 97...)/3! * 97!

==> (100 * 99 * 98)/3!

==> (100 * 99 * 98)/6

==> 161700

Value of 100C97.

==> (100!)/97! * 3!

==> (100 * 99 * 98 * 97...)/97 * 96 * ... * 3 * 2

==> (100 * 99 * 98)/3 * 2

==> 161700

Hence, the result is 161700.

Answer 2

Answer:-

➣

$\bf{100{C_{97}} = 161700}$

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• Given:-

${100{C_{3}} = 161700}$

• To Find:-

${100{C_{97}}=?}$

• Solution:-

We know:-

$\boxed{\bf{nC_{r}=nC_{n-r}}}$

Here,

$n=100 \\ C= 3$

Therefore,

$100C_{3} = 100 C_{100-3}$

$\: \: \: \: = 100C_{97}$

Hence,

$100C_{3} = 100C_{97}$

Therefore, the value of $\bf{100C_{3}}$ will be equal to $\bf{100C_{97}}$

We already know the Value of ${100C_{3}=161700}$

$\large \therefore{100C_{97}}={\bf{161700}}$

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