If 16Cr = 16Cr + 2, find rC4.

1.	If 16Cr = 16Cr + 2, find rC4.
Answer» Given, ¹⁶C_r = ¹⁶C_{r + 2} We know that, If ⁿC_p = ⁿC_q, Then one of the following conditions need to be satisfied : i. p = q ii. n = p + q From the problem, ¹⁶C_r = ¹⁶C_{r + 2} We can say that, ⇒ r ≠ r + 2 So, the condition(ii) must be satisfied, ⇒ 16 = r + r + 2 ⇒ 2r = 14 ⇒ r = \(\frac{14}{2}\) ⇒ r = 7. ∴ The value of r is 7.

Answer»

Given,

¹⁶C_r = ¹⁶C_{r + 2}

We know that,

If ⁿC_p = ⁿC_q,

Then one of the following conditions need to be satisfied :

i. p = q

ii. n = p + q

From the problem,

¹⁶C_r = ¹⁶C_{r + 2}

We can say that,

⇒ r ≠ r + 2

So, the condition(ii) must be satisfied,

⇒ 16 = r + r + 2

⇒ 2r = 14

⇒ r = \(\frac{14}{2}\)

⇒ r = 7.

∴ The value of r is 7.

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