3. What is∑


(
), where

is the number of ways of choosing k items from 28
items?
a. 406 *


b. 306 *


c. 28 *


d. 56 *

• no of ways of choosing k items from 28= 28ck
  therefore a=28ck
  so k can be from minimum 1.
  if k=1, 28c1=>28
  if k=2, 28c2=>378
  and so on.....
  thus, starting from minimum 28only ,so (28*something) should be the result
• 11 years agoHelpfull: Yes(11) No(2)
• 406*2^27 will be answer of it
• 11 years agoHelpfull: Yes(8) No(6)
• Consider (1+x)n=C0+C1x+C2x2+…..+Cnxn …….(1)
  Differentiating w.r.t x we get
  n(1+x)n−1=C1+2C2x+3C3x2+…..+nCnxn−1
  Multiplying by x on both sides,
  x.n(1+x)n−1=x.C1+2C2x2+3C3x3+…..
  Now again differentiating w.r.t to x
  n(1+x)n−1+n(n−1)x(1+x)n−2=C0+22C1x+32C2x2+42C3x3…..
  Putting x = 1, we get
  n(n+1)2n−2=C1+22C2+32C3+42C4
  Now substituting n = 28
  28(28+1)228−2 = 812.226 = 406.227
  
• 10 years agoHelpfull: Yes(0) No(0)