Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Determine n if ^2n C _3 : ^n C _3 = 12 : 1

Q.2.     Determine n if

            (i)\; ^{2n}C_{3}:^{n}C_{3}=12:1

Answers (1)

best_answer

Given that : (i)\; ^{2n}C_{3}:^{n}C_{3}=12:1

              \Rightarrow \, \, \frac{^{2n}C_3}{^nC_3}=\frac{12}{1}

The ratio can be written as

   \Rightarrow \, \, \frac{\frac{2n!}{(2n-3)!3!}}{\frac{n!}{(n-3)!3!}}=\frac{12}{1}

 \Rightarrow \, \, {\frac{2n!(n-3)!}{(2n-3)!n!}}=\frac{12}{1}

  \Rightarrow \, \, \frac{2n\times (2n-1)\times (2n-2)\times (2n-3)!\times (n-3)!}{(2n-3)!\times n\times (n-1)\times(n-2)\times (n-3)! }=\frac{12}{1}

\Rightarrow \, \, \frac{2n\times (2n-1)\times (2n-2)}{ n\times (n-1)\times(n-2) }=\frac{12}{1}

\Rightarrow \, \, \frac{2\times (2n-1)\times 2}{ (n-2) }=\frac{12}{1}

\Rightarrow \, \, \frac{4\times (2n-1)}{ (n-2) }=\frac{12}{1}

\Rightarrow \, \, \frac{ (2n-1)}{ (n-2) }=\frac{3}{1}

\Rightarrow \, \, 2n-1=3n-6

\Rightarrow \, \, 6-1=3n-2n

\Rightarrow \, \, n=5

 

 

 

 

 

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Board Exams 2025: Guidelines issued for Class 10, 12 practicals
anam-khan

Board Exam Date Sheet 2025 Live: ICSE, ISC, CBSE, MP time table out; BSEB routine soon
anam-khan

Board exam dates 2025: CBSE, CISCE, UP, MP, Maharashtra, TN time table out; state-wise updates

Latest Question