If 30Cr+2 = 30Cr-2, then r equals :

Question

If 30Cr+2 = 30Cr-2, then r equals : (A) 8 (B) 15 (C) 30 (D) 32

Tardigrade Admin · Accepted Answer

Let 30Cr+2 = 30Cr-2 ......(1) We know, If nCr1 = nCr2 then r1 + r2 = n In above given equation (1) we have n = 30, r1 = r + 2, r - 2 = r2 ∴ r1 + r2 = r + 2 + r - 2 = 2r and n = 30 ∴ 2r = 30 ⇒ r = 15

Q. If $^{30} C_{r + 2} =^{30} C_{r - 2}$ , then r equals :

8

15

30

32

Let $^{30} C_{r + 2} =^{30} C_{r - 2}$ ......(1)
We know, If $^{n} C_{r_{1}} =^{n} C_{r_{2}}$ then $r_{1} + r_{2} = n$
In above given equation (1) we have
$n = 30, r_{1} = r + 2, r - 2 = r_{2}$
$∴ r_{1} + r_{2} = r + 2 + r - 2 = 2 r$ and $n = 30$
$∴ 2 r = 30 \Rightarrow r = 15$

Q. If 30Cr+2​=30Cr−2​, then r equals :

8

15

30

32

Let 30Cr+2​=30Cr−2​ ......(1) We know, If nCr1​​=nCr2​​ then r1​+r2​=n In above given equation (1) we have n=30,r1​=r+2,r−2=r2​ ∴r1​+r2​=r+2+r−2=2r and n=30 ∴2r=30⇒r=15

Q. If $^{30} C_{r + 2} =^{30} C_{r - 2}$ , then r equals :

Let $^{30} C_{r + 2} =^{30} C_{r - 2}$ ......(1)
We know, If $^{n} C_{r_{1}} =^{n} C_{r_{2}}$ then $r_{1} + r_{2} = n$
In above given equation (1) we have
$n = 30, r_{1} = r + 2, r - 2 = r_{2}$
$∴ r_{1} + r_{2} = r + 2 + r - 2 = 2 r$ and $n = 30$
$∴ 2 r = 30 \Rightarrow r = 15$