Solve: nCr−1nCr−2=71 then possible value of n?

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Solve: {^nC_{r-2}}{^nC_{r-1}} = {1}{7} then possible value of

Question

Solve: $\frac{^{n} C _{r - 2}}{^{n} C _{r - 1}} = \frac{1}{7}$ then possible value of n?

7

3

5

6

Views: 657 students

Found 4 tutors discussing this question

Charlotte Discussed

Solve:

\frac{^{n} C _{r - 2}}{^{n} C _{r - 1}} = \frac{1}{7}

then possible value of n?

9 mins ago

Discuss this question LIVE

9 mins ago

\frac{^{n} C _{r - 2}}{^{n} C _{r - 1}} = \frac{1}{7}

\frac{^{n} C _{r - 2}}{^{n} C _{r - 1}} = \frac{n !}{( r - 2 )! ( n - r - 2 )!} \cdot \frac{( r - 1 )! ( n - r + 1 )!}{n !}

(r - 1)! = (r - 1) (r - 2)!

(n - r + 2)! = (n - r + 2) (n - r + 1)!

∴ \frac{^{n} C _{r - 2}}{^{n} C _{r - 1}} = \frac{( r - 1 ) ( r - 2 )! ( n - r + 1 )!}{( r - 2 )! ( n - r + 2 ) ( n - r + 1 )!}

\frac{^{n} C _{r - 2}}{^{n} C _{r - 1}} = \frac{( r - 1 )}{( n - r + 2 )} = \frac{1}{7}

7 (r - 1) = n - r + 2

7 r - 7 = n - r + 2

8 r = n + 9

The values of r & n should be such that they should satisfy the equation.

If we take,

r = 2

n = 7

values satisfy the equation

8 (2) = 7 + 9

16 = 16

∴ n = 7

Correct option is A.

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Solve: $\frac{^{n} C _{r - 2}}{^{n} C _{r - 1}} = \frac{1}{7}$ then possible value of n?
Answer Type	Text solution:1
Upvotes	150