Question

If nCr = 210 , then the value of 'n' is​

Answer 1

Answer

n=10

step by step

We have,

n P

r

=

5040

and

n C

r

=

210

,

(n−r)!

n!

=

5040and

(n−r)!r!

n!

=

210

Divide both

⇒ r!= 24⇒ r= 4

So

(n−4)!

n!

=

5040

⇒

(n−4)!

n(n−1)(n−3)(n−4)!

= 5040

⇒ n(n− 1)(n− 2)(n− 3)= 5040

⇒ n= 10

thank u for asking

❤ruhi✌✌

Answer 2

Answer:

The value of n = 21

Step-by-step explanation:

Given,

nCr = 210

To find,

The value of 'n'

Recall the concept:

nCr = $\frac{n!}{r!(n-r)!}$

Solution:

nCr = 210 ⇒nCr = 21×10

⇒nCr =$\frac{21X20}{2}$

Multiplying 19! with numerator and denominator we get,

$\frac{21X20}{2} = \frac{21X20X19!}{2X19!}$

= $\frac{21!}{2!X19!}$

= ₂₁C₂ 0r  ₂₁C₁₉

nCr =  ₂₁C₂ ,  ₂₁C₁₉

Comparing,

The value of n = 21

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