A student is allowed to choose at most n books from a collection of 2n+1 books. If the total number. of ways in which he can select atleast one book is 255, then the value of n is

Question

Accepted Answer

Correct answer: A. (a) Since number of ways of taken book from (2n+1 ) books can be given as ^2n+1C_1+ ^2n+1C_2+ ^2n+1C_3+ … . .+ ^2n+1C_n=x ( Let ) ∵ ^2n+1C_0+ ^2n+1C_1+ ^2n+1C_2+ … . .+ ^2n+1C_n+ … . + ^2n+1C_2n+1=2^2n+1 ⇒2x+ ^2n+1C_0+ ^2n+1C_2n+1=2^2n+1 ( ∵ ^nC_n-r= ^nC_r) ⇒2x+2=2^2n+1 ( ∵ ^nC_0= ^nC_n=1) ⇒x=2^2n-1=255 ( given ) ⇒2^2n=256=2^8 ⇒n=4 Hence, option (a) is correct.

$A student is allowed to choose at most n books from a collection of 2 n + 1 books. If the total number. of ways in which he can select atleast one book is 255, then the value of n is$

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