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mathmath333
 one year ago
Counting question
mathmath333
 one year ago
Counting question

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \color{black}{\begin{align} & \normalsize \text{A student is allowed to select at most n books } \hspace{.33em}\\~\\ & \normalsize \text{from a collection of (2n+1) books. if the total number } \hspace{.33em}\\~\\ & \normalsize \text{of ways in which he can select at least one book is 63.find n} \hspace{.33em}\\~\\ & a.)\ 4 \hspace{.33em}\\~\\ & b.)\ 3 \hspace{.33em}\\~\\ & c.)\ 5 \hspace{.33em}\\~\\ & d.)\ 6 \hspace{.33em}\\~\\ \end{align}}\)

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440601651278:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0@Nnesha can you help with this?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5you want to solve for \(n\) in : \[2^n1 = 63\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5no wait, they made it tricky

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5lets do it step by step

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1here is one of the link i didnt understand the answer given http://www.meritnation.com/askanswer/question/astudentisallowedtoselectatmostnbooksfromacolle/sets/2913008

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5forget that link, it would be easy if u try it on ur own

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5how good are u with pascal triangle ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1i just only know how to form a pascal triangle 1 121 1331...

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5lets review one important result of pascal triangle quick

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5``` 1 11 121 1331... ``` add the entries in first row, you get : 1 = 1 = 2^0 add the entries in second row, you get : 1+1 = 2 = 2^1 add the entries in third row, you get : 1+2+1 = 4 = 2^2

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5can you guess the sum of entries in 100000th row ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5Yes, but that looks ugly to have different numbers for index and exponent we can fix it easily, if we say that we start counting the rows from "0"

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5dw:1440602644567:dw

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1i didnt understand , do u mean i need to start couting from second row

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5now we can say that the sum of entries in \(n\)th row is \(2^n\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1ok if we count from the second row as row 1

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5Exactly, in other words we're starting our count for rows from 0,1,2,...

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5instead of 1,2,3,...

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5so when somebody asks you to look at "3"rd row of pascal triangle, they really mean the 4th row ok

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5can you tell me the sum of entries in row 6 and also the sum of entries in row 7 dw:1440602907133:dw

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1sum of 6th row =\(2^{6}\) sum of 7th row =\(2^{7}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5good, how is pascal triangle related to combinations/counting ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5suppose you have \(6\) objects how many total ways are there to choose 2 out of them ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5simplify, what is the number

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5Yes, now look at the 6th row in pascal triangle : dw:1440603215894:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5suppose you have \(6\) objects how many total ways are there to choose 3 out of them ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5you can guess, it is there in pascal triangle : dw:1440603390646:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5\(\large \binom{6}{4}\) is the number locatd at 4th position in 6th row (we count from 0)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5using pascal's triangle, can you tell the value of \(\dbinom{7}{5}\) ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1yes it is same as \(\binom{6}{2}=\binom{6}{4}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5Yes, it has that symmtry the values in left half are same as the values in right half

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.17th row 5th number or 2nd number

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5can you highlight the number

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1sry it was sry it was 3ed number 21

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5\(\dbinom{7}{5}\) is the 5th element in 7th row : dw:1440603778591:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.5so basically you want to solve : \[\large \dfrac{2^{2n+1}}{2}1 = 63\]
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