If displaystyle∑ k =110 K 2(10 C K )2=22000 L, then L is equal to

Question

If displaystyle∑ k =110 K 2(10 C K )2=22000 L, then L is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

displaystyle∑ K =110 K 2( 10 C K )2 displaystyle∑ K =110( K ⋅ 10 C K )2= displaystyle∑ K =110(10 ⋅ 9 C K -1)2 =100 displaystyle∑ K =110 9 C K -1 ⋅ 9 C 10- K =100( 18 C 9)=100((18 !/9 ! 9 !)) ⇒ 4862000=22000 L Hence L =221

Q. If $k = 1 \sum 10 K^{2} (1 0_{C_{K}})^{2} = 22000 L$ , then $L$ is equal to

$K = 1 \sum 10 K^{2} (^{10} C_{K})^{2}$
$K = 1 \sum 10 (K \cdot^{10} C_{K})^{2} = K = 1 \sum 10 (10 \cdot^{9} C_{K - 1})^{2}$
$= 100 K = 1 \sum 10^{9} C_{K - 1} \cdot^{9} C_{10 - K}$
$= 100 (^{18} C_{9}) = 100 (\frac{18 !}{9 ! 9 !})$
$\Rightarrow 4862000 = 22000 L$
Hence $L = 221$

Q. If k=1∑10​K2(10CK​​)2=22000L, then L is equal to

K=1∑10​K2(10CK​)2 K=1∑10​(K⋅10CK​)2=K=1∑10​(10⋅9CK−1​)2 =100K=1∑10​9CK−1​⋅9C10−K​ =100(18C9​)=100(9!9!18!​) ⇒4862000=22000L Hence L=221

Q. If $k = 1 \sum 10 K^{2} (1 0_{C_{K}})^{2} = 22000 L$ , then $L$ is equal to

$K = 1 \sum 10 K^{2} (^{10} C_{K})^{2}$
$K = 1 \sum 10 (K \cdot^{10} C_{K})^{2} = K = 1 \sum 10 (10 \cdot^{9} C_{K - 1})^{2}$
$= 100 K = 1 \sum 10^{9} C_{K - 1} \cdot^{9} C_{10 - K}$
$= 100 (^{18} C_{9}) = 100 (\frac{18 !}{9 ! 9 !})$
$\Rightarrow 4862000 = 22000 L$
Hence $L = 221$