If 5Cr-r- 5Cr-1- then the number of values of r is

Given : nbsp;^5C_r=r· ^5C_r 1 ⇒ ^5C_r ^5C_r 1=r ⇒ 5 r+1r=r (since ^nC_r ^nC_r 1=n r+1r) ∴ r^2+r 6=0 ⇒ (r+3)(r 2)=0 r= 3,2 rejecting r= 3 as r∈𝕎 ∴ Number of ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Permutations and Combinations

If 5Cr=r· 5Cr...

Question

If $^{5} C_{r} = r \cdot^{5} C_{r - 1}$ , then the number of value(s) of $r$ is

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $1$
Given : $^{5} C_{r} = r \cdot^{5} C_{r - 1}$
$\Rightarrow \frac{^{5} C_{r}}{^{5} C_{r - 1}} = r$
$\Rightarrow \frac{5 - r + 1}{r} = r$ $(since \frac{^{n} C_{r}}{^{n} C_{r - 1}} = \frac{n - r + 1}{r})$

$∴ r^{2} + r - 6 = 0$
$\Rightarrow (r + 3) (r - 2) = 0$
$r = - 3, 2$
rejecting $r = - 3$ as $r \in W$
$∴$ Number of solution $= 1$

Suggest Corrections

Similar questions

Q. If

^{5} C_{r} = r \cdot^{5} C_{r - 1}

, then the number of value(s) of

r

Q. If,

\frac{1}{^{5} C_{r}} + \frac{1}{^{6} C_{r}} = \frac{1}{^{4} C_{r}}

, then the value of

r

equals to

Q. If

^{1}^{5} C_{3}_{r} =^{1}^{5} C_{r}_{+}_{3}

, then

r =

Q. If

\frac{1}{^{5} C_{r}} + \frac{1}{^{6} C_{r}} = \frac{1}{^{4} C_{r}},

then the value of

r

equals to

Q. If set

A = {(r, s) | r, s \in W}

, then the number of element(s) in set

A

such that

^{5} C_{r} \cdot^{6} C_{s} = 1

Join BYJU'S Learning Program

Explore more

Permutations and Combinations

Standard XI Mathematics

Join BYJU'S Learning Program

If 5Cr=r⋅ 5Cr−1, then the number of value(s) of r is

The correct option is B 1Given : 5Cr=r⋅ 5Cr−1 ⇒ 5Cr 5Cr−1=r ⇒ 5−r+1r=r (since nCr nCr−1=n−r+1r) ∴ r2+r−6=0 ⇒ (r+3)(r−2)=0 r=−3,2 rejecting r=−3 as r∈W ∴ Number of solution =1

If $^{5} C_{r} = r \cdot^{5} C_{r - 1}$ , then the number of value(s) of $r$ is