Quant Exam  >  Quant Questions  >  If 6 times the no. of permutations of n items... Start Learning for Free
If 6 times the no. of permutations of n items taken 3 at a time is equal to 7 times the no. of permutations of (n-1) items taken 3 at a time then the value of n will be?
Verified Answer
If 6 times the no. of permutations of n items taken 3 at a time is equ...

This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
If 6 times the no. of permutations of n items taken 3 at a time is equ...
Given:
6 times the number of permutations of n items taken 3 at a time = 7 times the number of permutations of (n-1) items taken 3 at a time.

To find:
The value of n.

Assumption:
We assume that n is a positive integer.

Solution:

Let's break down the problem into smaller steps:

Step 1:
Write the formula for the number of permutations of n items taken 3 at a time.
The number of permutations is given by the formula: P(n, 3) = n! / (n - 3)!

Step 2:
Apply the given condition to form an equation.
6 * P(n, 3) = 7 * P(n - 1, 3)

Step 3:
Substitute the formula from Step 1 into the equation from Step 2.
6 * (n! / (n - 3)!) = 7 * ((n - 1)! / ((n - 1) - 3)!)

Step 4:
Simplify the equation.
6 * (n! / (n - 3)!) = 7 * ((n - 1)! / (n - 4)!)

Step 5:
Cancel out common factors in the equation.
6 * n! = 7 * (n - 1)!

Step 6:
Expand the factorial terms.
6 * n * (n - 1) * (n - 2) = 7 * (n - 1)!

Step 7:
Cancel out common terms.
6 * n * (n - 2) = 7

Step 8:
Solve the equation for n.
6n^2 - 12n - 7 = 0

Step 9:
Use the quadratic formula to solve for n.
n = (-(-12) ± sqrt((-12)^2 - 4 * 6 * (-7))) / (2 * 6)
n = (12 ± sqrt(144 + 168)) / 12
n = (12 ± sqrt(312)) / 12

Step 10:
Simplify the square root.
n = (12 ± sqrt(4 * 78)) / 12
n = (12 ± 2 * sqrt(78)) / 12
n = 1 ± sqrt(78) / 3

Step 11:
Since n is a positive integer, we discard the negative solution.
n = 1 + sqrt(78) / 3

Final Answer:
The value of n is approximately 3.48.
Community Answer
If 6 times the no. of permutations of n items taken 3 at a time is equ...
Options are - a 7 b 13 c 21 d 9
Explore Courses for Quant exam

Similar Quant Doubts

If 6 times the no. of permutations of n items taken 3 at a time is equal to 7 times the no. of permutations of (n-1) items taken 3 at a time then the value of n will be?
Question Description
If 6 times the no. of permutations of n items taken 3 at a time is equal to 7 times the no. of permutations of (n-1) items taken 3 at a time then the value of n will be? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If 6 times the no. of permutations of n items taken 3 at a time is equal to 7 times the no. of permutations of (n-1) items taken 3 at a time then the value of n will be? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 6 times the no. of permutations of n items taken 3 at a time is equal to 7 times the no. of permutations of (n-1) items taken 3 at a time then the value of n will be?.
Solutions for If 6 times the no. of permutations of n items taken 3 at a time is equal to 7 times the no. of permutations of (n-1) items taken 3 at a time then the value of n will be? in English & in Hindi are available as part of our courses for Quant. Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of If 6 times the no. of permutations of n items taken 3 at a time is equal to 7 times the no. of permutations of (n-1) items taken 3 at a time then the value of n will be? defined & explained in the simplest way possible. Besides giving the explanation of If 6 times the no. of permutations of n items taken 3 at a time is equal to 7 times the no. of permutations of (n-1) items taken 3 at a time then the value of n will be?, a detailed solution for If 6 times the no. of permutations of n items taken 3 at a time is equal to 7 times the no. of permutations of (n-1) items taken 3 at a time then the value of n will be? has been provided alongside types of If 6 times the no. of permutations of n items taken 3 at a time is equal to 7 times the no. of permutations of (n-1) items taken 3 at a time then the value of n will be? theory, EduRev gives you an ample number of questions to practice If 6 times the no. of permutations of n items taken 3 at a time is equal to 7 times the no. of permutations of (n-1) items taken 3 at a time then the value of n will be? tests, examples and also practice Quant tests.
Explore Courses for Quant exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev