Question

if 16 c 4 = 16 C r+ 2 , then find r c4

Answer 1

Answer:

We know the formula that,

If nCx = nCy, then x = y or x + y = n

According to the question,

16C4 = 16Cr+2

⇒ 4 + r + 2 = 16

⇒ 6 + r = 16

⇒ r = 16 - 6 = 10

Hence the value of r is 10.

Now we are required to rC4.

Substituting the values we get,

⇒ 10C4 = 10! / ( 10 - 4 )! 4!

⇒ 10C4 = 10! / 6! . 4!

⇒ 10C4 = 10 × 9 × 8 × 7 × 6! / 6! . 4!

⇒ 10C4 = 5040 / 4! = 5040 / 24 = 210

Hence the value of rC4 = 210.